In a large bowl, whisk flour, baking powder, baking soda, and salt. In the large bowl of a stand mixer fitted with the paddle attachment (or in a large bowl using an electric mixer), beat butter and granulated sugar on medium-high speed until creamy. Add eggs one at a time, beating well after each addition. Mix in almond and vanilla extracts.
Add dry ingredients and beat until just combined. Cover bowl with plastic wrap and refrigerate until well chilled, at least 1 hour or up to 2 days.
Preheat oven to 350° and line 2 baking sheets with parchment. Using a 1/2-cup measuring cup, scoop dough and roll into balls. Arrange on prepared baking sheets, spacing 4" apart.
Bake until edges are set and turning golden, 18 to 20 minutes. Let cool on sheets 5 minutes, then transfer to wire racks and let cool completely.