Preheat the oven to 350°F and line a large baking sheet with parchment paper.
Place ¼ cup of the Red Hots in a zip-top bag, seal, and crush gently with a rolling pin into coarse bits, leaving the remaining ¼ cup whole for topping.
In a large bowl, use an electric mixer to cream together the softened butter, granulated sugar, and cream cheese until the mixture is light, smooth, and fluffy.
Beat in the egg, vanilla extract, and almond extract until fully incorporated.
In a separate bowl, whisk together the flour, baking powder, and salt. Add the dry ingredients to the butter mixture and beat on low speed just until combined into a soft dough.
Gently fold the ¼ cup of crushed Red Hots into the dough using a rubber spatula. Cover and chill the dough in the refrigerator for about 30 minutes to make it easier to handle.
Place the powdered sugar into a small shallow bowl. Using a small cookie scoop or spoon, portion the chilled dough and roll into 1-inch balls. Roll each ball in the powdered sugar until completely coated.
Arrange the dough balls on the prepared baking sheet, spaced about 2 inches apart. Lightly flatten each ball with your fingers or the bottom of a glass, then press 2 to 3 whole Red Hots firmly into the center of each dough ball.
Bake for 9 to 11 minutes, until the edges are set. Do not overbake. The centers should still look soft and pale.
Let the cookies cool on the baking sheet for 5 minutes before moving them to a wire rack to cool completely.