Slice ½ cup (115 grams) of the butter into tablespoon sized pieces and place it in a light-colored skillet or saucepan.
Place the skillet over medium-low heat until the butter is completely melted.
Continue cooking, stirring the butter often with a rubber spatula. Once the butter is melted it will start to bubble/sputter, then become foamy. After that, small bits of milk solids will fall to the bottom of the pan, then quickly start to brown. The butter is browned once you see these brown bits of milk solids on the bottom of the pan and smell a nutty-aroma. If needed, you can increase the heat to medium to speed up the browning process.
Immediately remove the skillet from the heat and pour the butter into a heat-proof dish. Make sure to scrape out all of the browned bits from the bottom of the pan as well, this is where all of the flavor is at!
Transfer to the refrigerator uncovered until the butter is solidified, but not too cold. If the browned butter gets too cold, just place it back on the counter so that it can come to room temperature before mixing together the frosting. Place the other stick of butter on the counter to soften during this time.
Once the browned butter and butter have come to room temperature, add them to the bowl of a stand mixer fitted with the paddle attachment (or a large mixing bowl if using a handheld mixer). Beat the butters together on medium speed until smooth.
Mix in half of the powdered sugar on low speed until fully combined, then mix in the remaining half of the powdered sugar.
Add the heavy whipping cream, vanilla extract, and salt and mix on low-medium speed until fully combined, making sure to stop and scrape down the sides of the bowl as needed.
Use to frost cupcakes, cakes, etc.
Notes
Storage Instructions: Frosting may be stored in an airtight container in the fridge for up to 4 days.Freezing Instructions: Frosting will freeze well for up to 3 months. Thaw overnight in the fridge and bring to room temperature before using it.