Use the butter paper to grease the sides and bottom of a 9x13-inch glass baking dish.
Add the butter pieces and chocolate chips & squares to a large mixing bowl or stand mixer.
In a small saucepan, heat the milk and sugar together at a rolling bowl for 10 minutes, stirring constantly. Don't let the milk scorch or burn. After 10 minutes, remove from heat and pour over the butter and chocolate chips and mix well for at least 3 minutes and fudge base is smooth. Stir in the vanilla until incorporated.
Pour the fudge base into the baking dish and let cool for at least one hour in the fridge.
Add the frosting in a thin layer over the fudge and then cut into serving sizes. OR, cut the fudge and add tiny dollops of the frosting onto each fudge piece.
Serve German Chocolate Fudge chilled or at room temperature.