Place the 1 cup salted butter in a medium-sized, light-colored saucepan (a lighter pan will help you see the color change). Turn the heat to medium. Stir the butter occasionally as it melts to ensure even cooking.
After the butter has melted, it will begin to foam. Continue cooking over medium heat, stirring constantly with a spatula or spoon. This will prevent the milk solids in the butter from sticking to the bottom and burning.
As you cook, the butter will change from a pale yellow to a light tan, and finally to a deep golden-brown color. You may also notice a nutty aroma. Once the butter turns brown, immediately remove it from the heat to prevent burning.
Pour the browned butter into a heatproof dish to stop it from cooking and let it cool. It doesn't need to completely solidify but you do want it to become thickened.
Once the browned butter has cooled, In a large mixing bowl, use a hand mixer or stand mixer to beat butter until light and fluffy, 2 to 3 minutes.
Add in vanilla extract and mix until combined and smooth.
Add in powdered sugar 1/2 cup a time, mixing in between additions until smooth.
Frost immediately or store covered in an airtight container.