Preheat oven to 350F. Line 2 baking sheets with parchment paper.
Beat together strawberry cake mix, eggs, and oil until no lumps remain. Stir in mini chocolate chips.
Drop by tablespoonsfuls onto the baking sheets. Bake 8 - 10 minutes, rotating the sheets halfway through. Cool completely before frosting.
To make the frosting:
Whisk flour into the milk in a small saucepan over low heat. Continue whisking as it thickens to about the thickness of brownie batter. Remove from heat and stir in vanilla. Cool completely before proceeding.
Beat butter and sugar together until light and fluffy. Add cooled flour mixture and beat until everything is combined and it looks almost like whipped cream. If it separates, you just haven't beaten it enough - keep going!
To assemble:
Use an offset spatula to spread the frosting on a cookie and top with another cookie. Roll the cookie in sprinkles to cover the frosting.