In the bowl of a stand mixer, beat together butter and sugar until creamy. Beat in egg and vanilla until combined. Add beer and beat until well-combined.
Add flour, baking soda, baking powder and cornstarch to the stand mixer. Beat until combined.
Scoop out 1-inch balls of dough onto a silicone mat or parchment paper lined baking sheets. Chill for 20 minutes in the refrigerator.
When ready to bake, preheat oven to 350 degrees. Bake for 8 to 10 minutes. Cool cookies on wire racks.
In a large bowl, beat together frosting ingredients until creamy and smooth. Frost cooled cookies and top with sprinkles as desired.