Preheat oven to 350 degrees. Line 16 muffin tins with paper cupcake liners.
Use electric mixer to beat butter and sugar until lightened and fluffy, about 2 minutes. Then beat in vanilla and almond extracts.
On low speed, mix in eggs, one at a time, until well incorporated. Scrape down sides as needed.
In a small bowl, stir together flour, salt, cornstarch, baking powder and baking soda. Alternate beating in flour mixture and buttermilk, in 2-3 additions, starting and ending with flour mixture.
Fold in sour cream until well incorporated.
Place 1-2 teaspoons of batter into the bottom of each cupcake liner. Then place a frozen cookie dough ball in each liner (you will not use all of the cookie dough balls).
Cover cookie dough balls with batter so that each muffin tin is about 2/3 of the way full.
Bake for 14-17 minutes, or until tops are golden brown. Let cool completely before decorating.