Place the powdered sugar in a large mixing bowl or the bowl of a stand mixer and set aside. Measure out the milk and vanilla and set aside.

Heat the stick of butter in a small saucepan over medium heat, stirring very frequently. When the butter melts, stir constantly. The butter will get clear and yellow and then very suddenly become frothy, turn brown, and smell like caramel. When this happens, remove from heat.

Add the milk/vanilla mixture to the powdered sugar. Add the butter and mix with an electric or stand mixer until combined. The frosting will probably feel very wet and heavy at first--if you're frosting a sheet cake or cinnamon rolls, now is a great time to add the frosting. Otherwise, allow the frosting to cool (and it will become thicker and will hold its shape.) Serve as desired.