Cut the unsalted butter into small pieces. Heat a medium skillet over medium-low heat. Place the pieces of butter into the skillet.
Cook, stirring frequently, as the butter melts. It will begin to foam up. Keep stirring.
Cook for an additional 5-6 minutes, stirring constantly. The foam will subside and the milk solids will settle to the bottom of the pan and turn brown. Stir to prevent the milk solids from burning.
Once the butter turns an amber color and has a nutty aroma, remove it from the heat and pour into a heat-proof bowl. Let cool and solidify before continuing.
Add the softened cream cheese and solidified browned butter to a large mixing bowl.
Beat until smooth, about 2 minutes.
Add the vanilla extract and salt and mix to combine, about 1 minute.
Gradually add the powdered sugar, and beat until smooth and creamy and you've reached your desired consistency. If for some reason you need to thin out the icing, add a tablespoon of milk. If you want your icing to be thicker to pipe onto cupcakes, you may want to add more powdered sugar, a few tablespoons at a time.
Use brown butter cream cheese frosting to frost cakes, cupcakes, cookies and more. Refrigerate until ready to use.