In a stainless steal or light colored ceramic saucepan, melt ½ cup (1 stick) butter over medium heat. (You will want to be able to see the color changing in the butter.)
As the milk solids in the butter will start to foam, gently stir the butter.
The milk solids will subside then start to brown. You should start to smell the aromatic nutty flavors. (this takes anywhere from 5-10 minutes over medium heat. It can take 15 minutes over medium low heat)
Remove butter from heat and set aside to cool. If you have any small brown bits that is ok, but if there are any burnt bits you will want to strain the butter in cheesecloth.
Place plastic wrap in a bowl and pour room temperature butter into bowl.
Set butter in fridge until solid. (about 3 hours)
Remove butter from fridge and allow it to come to room temperature. (about 2 hours) Do not microwave.
Place room temperature butter and room temperature browned butter into mixer and using whisk attachment, whip for about 1 minute on medium high.
Add in sugar and vanilla and whip on low speed. Slowly, 1 tablespoon at a time, add in buttermilk. I usually use about 4 tablespoons but have used as many as 6. Whip frosting on high for 1-3 minutes, until it