Let the brown butter cool to room temperature. Meanwhile, remove your cream cheese from the fridge so it can come to room temperature too.
Once the brown butter and cream cheese are both at room temperature, beat them together until smooth.
Sift in the powdered sugar and mix in slowly. You may need more powdered sugar depending on your cream cheese - see notes.
Add the vanilla, and a pinch of salt if using unsalted butter, and beat at medium-high speed for 1-2 minutes or until creamy.
Notes
If you are using spreadable cream cheese from a tub, instead of a block of cream cheese, you may need more powdered sugar in order to thicken the frosting enough. Add an extra cup (120g) of powdered sugar. You can also chill the frosting once it has been mixed together in order to make it a little stiffer before decorating your cakes.