Preheat an oven to 350 degrees F (175 degrees C). Line 24 muffin cups with paper muffin liners. Divide sugar cookie dough into each muffin cup.
Bake in the preheated oven until the cookie dough softens and spreads across the bottom of each muffin cup, 8 to 10 minutes. Remove from oven and set aside.
Beat the cream cheese, sour cream, sugar, flour, and milk with an electric mixer in a large bowl until smooth. Beat the first egg into the cream cheese mixture until completely blended, then beat in the last egg. Mix in the instant pudding mix until just incorporated. Spoon about 2 tablespoons of the cream cheese filling into each muffin cup. Return muffin cups to the oven and bake until the filling is set, about 25 minutes. Cool in the pans for 30 minutes then remove the desserts.
Remove the foil cover of the prepared frosting and microwave until softened, about 30 seconds. Stir frosting until smooth, then spread about one tablespoon of frosting onto each dessert cup. Refrigerate until set, about 1 hour.