Stir the yeast into the warm water and let sit for 5 minutes.: You should notice tiny bubbles forming and a yeasty aroma as the mixture becomes frothy; this indicates active yeast . If nothing happens, the yeast may be old or the water too hot or cold, and you should start over to avoid dense dough. Proper activation ensures the dough rises predictably.
In a mixing bowl, combine milk, sugar, and salt. Using a mixer with a paddle attachment, beat in eggs one at a time, stopping to scrape down the sides of the bowl after each addition.: The batter will look glossy and slightly thick as the eggs emulsify with the milk and sugar , and you should hear a steady motor hum from the mixer; it helps incorporate air. Scraping prevents pockets of unmixed ingredients. If you skip scraping, you may end up with uneven texture in the dough.
Beat in shortening and 2 cups of flour.: At this point the bowl will feel heavier and the mixture will start to take on body, with the shortening creating a satiny texture. Adding the first measure of flour gives the dough structure without becoming stiff. Overworking now can develop too much gluten, making the final donut tough.
In a small bowl, stir together cocoa powder and food coloring to make a paste.: The paste should be smooth and intensely colored, and the cocoa aroma will sharpen. Making a paste prevents streaks and ensures even distribution of the red liquid food color . If the paste is lumpy, strain or remix to avoid speckled dough.
Add food coloring paste to dough and mix well.: As the paste blends in, the dough will deepen to a red hue and you may smell the cocoa more distinctly; this visual cue signals even color. Mix until you have uniform shading without overmixing. Incomplete mixing yields marbled color and inconsistent flavor.
Keep adding flour, 1/2 cup at a time, until dough begins to pull away from sides of bowl.: The dough will transition from sticky to tacky and you will see it start to climb the paddle a little, signaling the right consistency for kneading. Adding flour gradually prevents over-drying. Adding too much at once risks a dry, crumbly dough.
Switch to a dough hook and knead dough for 5 to 8 minutes, until soft but not sticky.: You will hear a change in the mixer tone as the dough becomes smoother and more elastic, and it should feel supple to the touch. Proper kneading develops gluten for structure and chew without making the crumb tight. Under kneading produces a slack dough that will not hold its shape in the fryer.
Place dough in a lightly oiled bowl, turning dough to coat it in oil.: Coating the surface prevents crust formation during the rise, and the dough will glisten faintly where the oil touched it. This keeps the exterior soft and encourages even rising. Forgetting to oil the bowl can create a dry film that inhibits full expansion.
Cover bowl with plastic wrap and let rise until it doubles in bulk, about 1 1/2 hours.: Look for a visible increase that is pillowy and soft to the touch, with small surface bubbles; that indicates sufficient fermentation. The aroma will become slightly fermented and sweet. If it does not double, give it more time in a warmer spot, as rushing will produce dense donuts.
Fill a Dutch oven with about 2 inches of oil and heat to 350 degrees.: The oil should shimmer slightly and register steady at 350 degrees , which creates fast set of the exterior while cooking the interior. Use a thermometer to maintain temperature, and avoid overcrowding which drops the oil temp. Oil below target yields greasy donuts, while too hot will brown too quickly without cooking through.
Cut dough into four pieces, and working 1 piece at a time, roll dough out on a lightly floured surface to a thickness of 1/4-inch. Use a 3-inch round cookie cutter and a small round cutter to cut donuts. You can use the small round cutter to make more donut holes out of the scraps.: The rolled dough should feel springy and hold the cut edges cleanly; the donuts should relax slightly before frying. Keep scraps covered to prevent drying as you work. Rolling too thin makes fragile donuts that absorb oil, and rolling too thick leads to undercooked centers.
Carefully slide a few donuts into the oil. Fry for 35 to 45 seconds and then flip over. Cook the second side about 30 seconds and then place on a rack or a paper towel-lined baking sheet.: Listen for a gentle sizzle that quiets as the donut cooks, and look for a light golden edge before flipping; the interior will remain soft and aromatic. Draining on a rack prevents sogginess from trapped steam. Frying too many at once will lower oil temperature and create oily, undercooked donuts.
For glaze, combine confectioners' sugar, milk, and vanilla extract in a bowl and whisk until smooth.: The glaze should be velvety and pourable, without lumps, and it will have a sweet milky scent with vanilla notes. A smooth glaze sets quickly into a glossy shell on warm donuts. If the glaze is too thick add a splash more milk , and if too thin add more confectioners' sugar ; avoid adding too much liquid at once.
Drizzle glaze on top of donuts.: The warm donuts will take the glaze and create a thin, shiny coat that slightly firms as it cools, giving a pleasant bite. Use a spoon or fork to control coverage and allow excess to drip off before stacking. Donuts that are too hot may melt the glaze into a thin coat, while donuts too cool may not take the glaze evenly.
