Melt the butter in a light-colored pan (like stainless steel) over medium heat, stirring frequently, until golden brown specks form and the butter gives off a rich, nutty aroma. Remove from the heat right away.
Pour the browned butter into a separate bowl and let it cool slightly. Refrigerate until it starts to thicken and becomes partially solidified.
Add the cooled brown butter, cream cheese, vanilla extract, and salt to a large mixing bowl, then use an electric hand mixer to beat until creamy and well combined.
Gradually mix in the powdered sugar and continue beating until the frosting is light and fluffy.