In a large bowl, whisk together the flour, baking powder, and salt. Set aside. In another large mixing bowl, use an electric mixer to cream the softened butter and sugar until the mixture is light and fluffy. Add the eggs one at a time, ensuring each is fully incorporated before adding the next. Mix in the vanilla extract and almond extract until well combined.
Gradually add the dry flour mixture to the butter and sugar mixture. Mix on low speed until a soft dough forms, being careful not to overmix. Divide the dough into two equal portions, then place each portion on a piece of parchment paper or a silicone mat dusted lightly with flour. Using a floured rolling pin, roll each portion to about ¼-inch thickness. Add more flour as needed if the dough sticks.
Dust the surface of the dough lightly with flour, cover with plastic wrap, and chill for at least 1–2 hours, or leave overnight for best results.
Preheat the oven to 375°F (190°C). Line two or three large baking sheets with parchment paper or silicone mats. Remove one portion of dough from the refrigerator and use cookie cutters to cut out your desired shapes. Arrange the cut-out cookies about 2–3 inches apart on the prepared baking sheets. Re-roll the scraps as needed to cut more cookies, but ensure the cut dough is chilled in the refrigerator or freezer for at least 10 minutes before baking to prevent spreading.
Bake the cookies in the preheated oven for 8–10 minutes, or until the edges are just lightly golden. Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.