In a separate bowl, beat the butter, shortening, and sugar together until light and fluffy. Add the egg, sour cream, vanilla extract, and almond extract and beat again, scraping down the sides of the bowl as needed.
Add the flour mixture in 2-3 smaller additions; mixing well after each addition. Wrap the dough with plastic wrap and chill in the refrigerator for 4 hours.
Preheat the oven to 350°F/175°C, line a cookie sheet with parchment paper and set aside. Remove the dough from the plastic wrap to a floured surface and use a rolling pin to roll it to a thickness of ½”.
To prepare the frosting, beat the butter until light and fluffy, then add the powdered sugar and beat again until smooth. Next, stir in the vanilla and salt.