Cream together the butter and sugar until fluffy, about 3 minutes. Add in the egg, sour cream and vanilla extract and mix until well combined.
Mix in the flour, cornstarch, baking powder, baking soda, and salt on low speed until just combined. Cover the mixing bowl with plastic or transfer the dough to a piece of plastic wrap and chill for 1 hour.
Preheat oven to 375º F. Roll the cookies to 1/4-inch thickness. Cut with a cookie cutter and place onto a parchment lined baking sheet. Bake 8 to 10 minutes until the edge of the cookie turns a slight beige. Remove from the oven and allow to cool completely.
Buttercream Frosting
Cream together the softened butter, shortening, and powdered sugar until fluffy, about 3 minutes. Add in the vanilla extract and half of the milk. Mix on low speed until combined. Slowly add the milk until the mixture is smooth. Then, turn the mixer to high speed until it is creamy and smooth. If using food coloring, beat a drop at a time until you achieve the desired color.
Once cookies are completely cooled, spread a layer of buttercream frosting on the cookies. Top with sprinkles, if desired.
Notes
The size cookie cutter used will determine the number of cookies. I used a 2 1/2- inch circular cookie cutter for 30 cookies.
Chilling the dough makes the cookie dough less sticky and easier to roll.
Butter and shortening in the buttercream gives the buttercream a delicious buttery flavor while making for a sturdier frosting on the cookie. You can use all butter, but note that the cookie frosting won't be as sturdy, or all shortening and note that you won't have the buttery undertones in the final frosting.
Storage Tips
Room Temperature: Store baked, cooled, and frosted cookies at room temperature for up to 3 days.
Refrigerate: Store in an airtight container in the refrigerator for up to a week.
Freeze: Freeze unfrosted baked cookies for up to 3 months. To freeze them, place them in a single layer with parchment paper between each cookie, then store them in a freezer-safe airtight container. Remove from the freezer to thaw and frost them once fully thawed.