Cut the butter into even sized pieces, so it melts evenly and at the same rate.
Place the butter in a light colored skillet over medium heat. Swirl the pan as it melts to help it heat evenly.
Once melted, the butter will foam and sizzle around the edges. Keep stirring or swirling occasionally during this stage.
As the foam starts to subside, watch closely, since the butter moves from foaming to browning quickly from this point. Look for small golden brown specks settling at the bottom of the pan and a nutty aroma. Stir the butter to keep the specks from settling on the bottom of the pan and burning.
As soon as the butter turns golden brown, smells toasty, and especially before the specks get too brown, remove the pan from the heat immediately and transfer the butter to a heatproof bowl, scraping in the browned bits from the bottom of the pan, since that is where most of the flavor is.
Set the brown butter aside to cool
Making the frosting
Using a hand mixer or stand mixer, soften cream cheese by mixing for about 30 seconds. Scrape down the sides and bottom of the bowl when finished.
Add cooled brown butter and combine until smooth.
Add sifted powdered sugar and vanilla extract and combine until smooth.