Cream sugar and butter together in a large bowl of a stand mixer afixed with an S blade or with a hand mixer. Mix until pale yellow, fluffy, and well-incorporated.: You will notice the bowl filling with a soft, pale cloud as the butter and sugar aerate; this lightness is crucial for tender cookies. The sound shifts from a soft whir to a slightly brisker, airy noise when enough air has been incorporated. If the mixture looks glossy or too loose, your butter might be too warm which makes shaping harder later. A common mistake is overcreaming which can lead to spread. Stop when the mixture is pale yellow and fluffy, scraping the bowl once so everything is evenly combined.
Add the egg yolks and lemon zest and mix until well-combined.: As you fold in the egg yolks and lemon zest , the aroma will shift, with citrus top notes rising and the mixture taking on a richer, silkier texture. The bowl should look glossy but not wet. The eggs help bind and enrich the dough, while the zest brings fragrance. Avoid overmixing at this point because excess gluten development can toughen the cookies; mix until the components are harmonized.
Sift the flour over the wet ingredients, and mix just until combined.: The first sniff of dry flour is mild and toasty. Sifting over the bowl lightens the flour as it falls in, encouraging even hydration without clumps. Blend until you see no streaks of flour, but stop short of a smooth batter; tiny crumbs are fine here because the dough will be gently worked next. A typical error is vigorous mixing which tightens the dough; gentle folding preserves tenderness.
Knead together very gently until it forms enough of a ball to plop onto a piece of plastic wrap. Work the dough just enough to get it to stick together, but be careful not to overdo it. Honestly, I get so paranoid about overworking the dough that I pile the crumbs onto the plastic wrap, fold it up around the mound, and press it together that way.: The dough will feel crumbly at first, then cohere under the warmth of your hands. I like to use the plastic wrap trick, piling the crumbs onto a sheet and folding it over to press into a uniform disk. This minimizes handling and prevents the butter from warming too much. If you knead aggressively, the cookies can become tough, so be cautious and light handed.
Completely wrap the dough with the plastic wrap and chill the dough for at least three hours.: Chilling firms the butter and lets the flours hydrate, which improves rolling and flavor melding. The dough becomes less sticky and easier to roll thin without tearing. If you skip this, the dough will spread and lose crisp edges. Plan ahead so the chilling time is not rushed, it's key to consistent shapes.
When you're ready to pull the dough out and prepare it, preheat oven to 350°F (175°C).: The oven warming produces a clean, comforting heat that pairs with the lemon notes in the dough. Preheating ensures the cookies begin setting immediately, which preserves their cut shape. If you underheat the oven, cookies may spread and lose definition. Give the oven time to fully reach temperature before baking.
Roll out dough – I go as thin as 1/8 inch, but I prefer about 1/4 inch thick. Cut into shapes, adding additional flour as necessary to avoid sticking. Place cookie shapes on a cookie sheet (no need to grease).: Rolling reveals the dough’s texture, a smooth surface that responds to gentle pressure. Thinner cookies will crisp more, while a quarter inch yields a tender interior, so choose based on your preference. Lightly flour the surface to prevent sticking, but too much flour can dry edges. Arrange shapes evenly on the sheet to allow even air circulation in the oven.
Bake just until the cookies start to turn pinky beige around the edges, around 8 minutes. Let cool for a couple of minutes on the baking sheet, then move to wire rack to cool completely.: The aroma will turn warmly buttery with a whisper of toasted flour as the edges color. Visual cues include tiny golden rims and a set top that no longer looks wet. Overbaking dries the crumb and ruins the tender interior, so watch closely in the final minutes. Cooling briefly on the sheet allows edges to firm without breaking, then transfer to a wire rack to cool completely.
To make the icing, add the powdered sugar, 2 tablespoons milk, corn syrup, and the vanilla to a small mixing bowl. Use a wire whisk or a fork to mix it well. If it's too thick, add more milk a teaspoon at a time. You want the icing to be thin enough to be pipeable but thick enough to hold a line. Transfer the icing into a piping bag with tip or a Ziploc bag with the end snipped off, and pipe the icing onto the cookies. Let the icing sit until it hardens before storing or assembling on cookie plates.: The powdered sugar will smell sweet and clean, and as you whisk, the mixture thins into a glossy, snow white glaze. The corn syrup lends shine and keeps the icing slightly elastic while the vanilla rounds the flavor. If the icing is too thick, add milk a teaspoon at a time; if too thin, add a little more powdered sugar. Avoid adding too much liquid at once, which can leave you with runny, unworkable icing.
Cookies keep up to one week in an airtight container.: The sound of the whisk is soft, and the bowl should reflect light as the glaze forms. When piping, steady pressure and a gentle wrist make clean lines, and the icing will settle into neat edges. Let the icing sit until it hardens before stacking; rushing this step can mar designs or cause smudging. If bubbles appear, a quick pop with a toothpick smooths them out.
Let the icing sit until it hardens before storing or assembling on cookie plates: The cookies will gradually lose their wet sheen and set to a delicate matte finish. This drying time is crucial for stacking or transporting cookies without damaging the surface. Store in an airtight container once firm, and avoid layering cookies until the icing is completely dry, as decorations can stick together.
Cookies keep up to one week in an airtight container: Proper storage preserves both texture and flavor, maintaining the tender crumb while keeping the icing intact. The container should be cool and dry; humidity can soften the icing. If you need longer storage, consider freezing uniced cookies, then icing after thawing to preserve the crisp finish.