In a medium saucepan over medium heat, melt butter until it turns golden in color and has a nutty aroma. Remove from heat and allow to cool 10-15 minutes.
Pour butter into a large mixing bowl,and gradually add in powdered sugar. Add milk and beat until smooth.
Notes
When you brown the butter, I find it's best to use a light colored pan so you can see when the butter starts to brown and it's less likely to burn.
Be sure to cool cookies and cakes before frosting them or you run the risk of it melting and sliding off.
If you prefer a runnier icing, add a little milk, a bit at a time, until you have the desired consistency.
The frosting can be frozen for up to 3 months in an airtight container. Thaw in the refrigerator and bring it up to room temperature before using.