Beat the butter and cream cheese at medium speed until mixed and fluffy, about 5 minutes. Scrape down the sides of the bowl.
Add the egg, almond extract, and vanilla extract. Beat again until smooth and creamy, about 5 additional minutes.
In a medium bowl, stir together the flour, baking powder, and salt. Add the flour mixture to the butter mixture, about ½ cup at a time, just until mixed.
Shape the dough into a rectangle and wrap with plastic wrap. Refrigerate overnight.
When ready to bake, preheat the oven 375 degrees. Prepare two or three large rimmed, baking sheets with parchment paper.
Roll out the cookie dough to ½ inch thick. Cut with cookie cutters and transfer to the baking sheet. Bake for 8 to 10 minutes or just until the edges are set and the cookies are puffed.
Allow the cookies to cool completely on the baking sheets. Decorate as desired.