Preheat oven to 350°F and line a baking sheet with parchment.
Melt butter in microwave, then mix in granulated and powdered sugar until smooth.
Add egg, yolk, vanilla, and cake batter extract; stir well.
Mix in baking powder, baking soda, and salt.
Gradually add flour until combined; fold in sprinkles.
Scoop dough into ¼-cup balls, roll and flatten slightly.
Bake 11–12 minutes until centers set; cool on sheet.
For frosting, beat butter and cream cheese until creamy.
Add vanilla, cake batter extract, powdered sugar; beat until fluffy. Add milk to thin if needed.
Frost cooled cookies and top with sprinkles.
