Melt your chocolate chips if you haven’t already and set aside to cool. You obviously don’t want it so cool that it hardens, but you can get it close to room temperature and still have it be soft and stir-able.

In a small saucepan, whisk together sugar, flour, cocoa, and milk; bring to a boil, whisking frequently. Boil 1-3 minutes or until thickened like a thinned pudding. Remove pan from heat and strain mixture into a small bowl. Cool completely in the refrigerator or freezer.

When chocolate flour mixture is cooled, beat the butter until creamy, about 1 minute. Beat in the cooled chocolate mixture until well combined fluffy, about 1 minute. Finally add in melted chocolate and beat again until well combined and fluffy, about 2 minutes. If desired, add additional cocoa powder to taste, up to 4 tablespoons more. Spread or pipe frosting on to cupcakes or cake.