Sift the flour, baking powder, baking soda, and salt together in a medium mixing bowl and set aside.
In a stand mixer or large mixing bowl add the butter and sour cream (BOTH AT ROOM TEMP) and cream together until nice and smooth. Add the sugar, eggs, vanilla, and almond extracts and mix until combined.
Add the dry ingredients to the wet ingredients in 3 batches, mixing in completely after each addition. Form a loose ball with the dough and place it in a covered bowl or wrapped in plastic in the fridge for 30 minutes.
After about 15 minutes, preheat your oven to 400°F and line your baking sheets with parchment paper or a silicone mat.
Once your dough has chilled, place it on a lightly floured surface and roll it out to ¼" thick. Cut out circles using a round cookie cutter or the top of a round glass (this is what I used). These won't spread so you don't have to space out too much but give them a little breathing room.
Bake the cookies one pan at a time for 6-8 minutes. The cookies will puff up a little but won't get very brown so don't panic. This is how they stay nice and soft. Remove from the baking sheet right away and cool completely on a rack before frosting.