In a medium bowl, mix (or sift together) the flour and baking powder. In a one-cup measuring cup, lightly beat the egg with the extracts.
In the bowl of a standing mixer (or in a large bowl with a handheld mixer), beat the butter and salt on medium speed until smooth. With the mixer running, gradually pour in the sugar; add the lemon zest. Beat on medium until fluffy, about 1 minute.
With the mixer running, pour in the egg mixture and continue beating until incorporated. Scrape down the sides of the mixer bowl. With the mixer on low, gradually add the flour and mix just until evenly blended.
Lightly knead the dough to form a ball, press it into a disk 1-inch thick, and wrap tightly in plastic wrap. Refrigerate for 2 hours or overnight. You can also freeze the dough at this point!
Line a baking sheet with parchment paper or a silicone baking mat. Adjust an oven rack to the middle position and heat the oven to 375 degrees F. If you’ve chilled the dough overnight, it’ll need to sit at room temperature for half an hour or so to soften slightly. If you've frozen the dough, thaw it in the fridge overnight then allow it to soften at room temperature.
On a very lightly floured sheet of wax paper with a sheet of plastic wrap on top of the dough, roll the dough out to ¼-inch thick. You can use rolling pin guides or wooden dowel rods as guides for achieving even cookie thickness. Cut cookies using a floured cookie cutter. Re-roll scraps, always using as little flour as necessary.
Bake the cookies, one sheet at a time, for 5-9 minutes, until they no longer look wet on top. The baking time will depend on the size of the cookies you’ve cut. You don’t want the bottoms to be browned, except for maybe just a bit on the edges.
Let the cookies rest for a couple minutes on the sheets before transferring them to cooling racks to finish cooling.