In a medium-sized bowl, combine flour, baking powder, and salt. Set aside.
Using an electric stand mixer, beat butter and sugar until smooth and creamy, about 2 minutes. Add eggs one at a time, beating to combine between each addition, vanilla extract, and almond extract; beat until combined. Reduce mixer speed and gradually spoon flour mixture in with butter mixture, beating on low speed until dough is smooth and well-blended.
Turn dough out on work surface. Cut dough in half and shape each portion into a compact disk. Wrap separately in plastic wrap and chill for 30 minutes to 2 hours.
Preheat oven to 375°F. Unwrap 1 dough disk and roll on lightly-floured work surface to ¼-inch thickness. Cut into chosen shapes and place cookies 2 inches apart on parchment paper-lined baking sheets. Refrigerate cookies on baking sheets for 5 to 10 minutes to help them keep their shape when baked.
Bake in preheated oven for 8 to 10 minutes, or until cookies just start to turn golden around the edges, rotating halfway through baking. Cool cookies completely on wire racks, about 20 minutes. Repeat process with remaining dough.
