Preheat the oven to 350°F. Line an 8×8 inch square pan with parchment paper so the bars lift out easily.
Open the cookie dough and press it evenly into the bottom of the pan. Smooth the top with slightly damp fingertips or an offset spatula.
Bake for 18 to 22 minutes until the edges are lightly golden and the center looks set. Avoid overbaking to keep the bars soft.
Cool completely before frosting so the topping does not melt.
In a medium bowl, beat the butter until fluffy. Add powdered sugar, cocoa powder, milk, and vanilla. Beat until creamy and smooth. Add a splash more milk if needed to help it spread easily.
Spread the frosting over the cooled cookie bar base. Add sprinkles across the top.
Chill for 15 minutes to help the frosting set. Lift the bars out of the pan and slice into squares.