Mix the dry ingredients. In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
Cream butter and sugar. In a large bowl using a stand mixer or hand mixer, beat the softened butter and granulated sugar on medium speed until light and fluffy, about 2 to 3 minutes. Scrape down the bowl.
Add egg and extracts. Beat in the egg, vanilla, and almond extract (if using) until fully combined. Scrape down the bowl again.
Bring the dough together. Add the dry ingredients and mix on low just until no dry streaks remain. The dough should look soft and cohesive, not crumbly. If it seems sticky, that is fine. It firms up as it chills.
Chill. Divide dough into two disks, wrap tightly, and refrigerate for at least 1 hour (and up to 2 days). This is the difference between clean cutouts and cookie puddles.
If your dough is very firm (especially after a day or two), let it sit at room temperature for 5 to 10 minutes so it is rollable without cracking.
Preheat and prep pans. Heat oven to 350°F. Line baking sheets with parchment or silicone mats.
Roll and cut. On a lightly floured surface (or between parchment), roll one disk to 1/4 inch thick. Cut shapes with cookie cutters and transfer to the prepared baking sheets, spacing about 1 inch apart.
Chill the cutouts (quick insurance policy). Pop the trays in the fridge for 10 to 15 minutes before baking, especially if your kitchen is warm or your shapes have lots of detail. (You can also freeze the cutouts on the tray until solid, then bag them and bake from frozen with 1 to 2 extra minutes.)
Bake. Bake for 9 to 11 minutes, until edges are set and the tops look matte (not shiny) with little to no color. For softer cookies, pull them when the tops still look a touch pale. Let cookies cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.
Reroll scraps. Press scraps together gently, chill for 10 minutes if they feel warm, then reroll and cut. Try not to add too much extra flour while rerolling.
Optional quick icing. Whisk powdered sugar, milk, vanilla, and salt until smooth. Adjust thickness: add a few drops of milk to thin, or a spoonful of powdered sugar to thicken.
Consistency cue: For a simple dip or glaze, you want a thick ribbon that melts back into the bowl in about 5 seconds. For spreading, keep it a bit thicker so it stays put on the cookie.
Dip cookies or spread icing with a spoon, then decorate with sprinkles before it sets.
Cool, set, and enjoy. Let icing fully set before stacking, usually 1 to 2 hours depending on thickness.
