In a large bowl, beat the butter, cream cheese, and sugar for 2-3 minutes at medium speed until smooth and creamy, scraping the sides of the bowl with a spatula a few times. Beat in the vanilla, almond extract, and egg.
Whisk together the flour, baking powder, and salt in a small bowl.
Dump the dry ingredients into the creamed mixture. Stir gently just until the flour is moistened.
Cover the sugar cookie dough or wrap in plastic wrap and chill for about an hour, or until stiff enough that it doesn't stick to your finger.
Preheat your oven to 375 degrees. Line cookie sheets with silicone mats or parchment paper, or spray with cooking spray.
Use a rolling pin to roll dough about 1/2" thick on a lightly floured surface. Cut out with cookie cutters.
Transfer cookies with a spatula to prepared baking sheets. Bake for 10-12 minutes at 375°. Cookies should be set, but they don't brown like other sugar cookies.
Let cool on pans for 3-5 minutes, then carefully transfer to wire racks to cool completely.