Preheat oven to 350ºF.: The warm air in the oven should feel steady and even when you open it, ensuring the phyllo shells crisp uniformly. I usually set a timer so I do not forget to preheat long enough, because an under heated oven will produce soggy bottoms. You will notice a clean, dry heat when it is ready. One common mistake is sliding the tray in too early, which prevents the phyllo from getting that delicate brown edge.
Remove rind from brie and cut into 30 pieces. Place each piece of cheese in mini phyllo tart.: As the brie warms from handling it becomes more pliable and easier to slice. I use a sharp knife and gentle sawing motions to keep pieces tidy, then nestle each piece into the center of a phyllo tart so it has room to melt without overflowing. The scent of the cheese will become more pronounced as you work. Avoid slicing too thinly, because scant pieces can disappear into the tart when melted.
Mix together pecans, brown sugar, and Kahlua. Spoon over brie.: When you stir the chopped pecans with the brown sugar and Kahlua , the mixture becomes glossy and aromatic, releasing a warm coffee and caramel scent. I use a small bowl and toss until the sugar coats the nuts evenly; the liquid should just moisten the sugar, not make it runny. This balance ensures the topping caramelizes without making the phyllo soggy. A frequent error is adding too much liquid, which leads to a wet topping rather than a sticky crumble.
Bake for 10 to 15 minutes, until cheese is melted.: Spoon small portions of the pecan mixture onto each tart so the topping sits atop the melting brie and does not overwhelm it. When you do this, you will see the contrast between the glossy nut mix and the pale cheese, and a sweet aroma will thread through the kitchen. I use a teaspoon for consistent amounts, because uneven portions can cause some tarts to overflow while others stay bare. Be mindful not to press the topping into the cheese, as the texture should remain distinct.
Bake for 10 to 15 minutes, until cheese is melted.: While baking, you will hear a faint whisper of crisping from the phyllo and smell the pecans toasting further. The brie should soften and look glossy, with the edges of the phyllo turning a light golden. I check at around 10 minutes and watch the cheese; once it is visibly melted and the shells have color, they are done. Leaving them too long can lead to overly dark edges or a very runny center that is hard to plate.