In a medium saucepan, whisk together the flour and milk over medium heat until thickened.

Remove the saucepan from the heat and let the mixture cool completely.

In a mixing bowl, beat the softened butter and granulated sugar together until light and fluffy.

Gradually add the cocoa powder to the butter mixture, mixing until fully combined.

Add the cooled flour mixture to your butter and cocoa mixture. Beat on medium speed until everything is well combined and smooth.

Mix in the vanilla extract.

If the frosting is too thick, add a splash of milk to reach desired consistency.

Spread the frosting generously on your cooled cake or cupcakes.