Start by browning the butter to bring a nutty depth to your Peach Buttercream Frosting. In a small heavy saucepan, melt the unsalted butter over medium heat, stirring constantly for about 8 to 10 minutes. You'll know it’s ready when it turns golden brown and has a fragrant aroma. Immediately remove the pan from heat and pour the butter into a small freezer-proof bowl. Cover and chill it until the butter cools and begins to solidify, which should take about an hour.
Next, prepare your peach puree, which will contribute the vibrant flavor to the frosting. Take the peeled and coarsely chopped fresh peaches and process them in a food processor until completely smooth. Strain the mixture through a fine mesh strainer into a bowl to eliminate any solids. Then, transfer the strained peach puree to a small heavy saucepan and cook over medium heat, stirring often, for 10 to 15 minutes until it reduces to about ½ cup. Allow the puree to cool completely for approximately 20 minutes after cooking.
Now comes the fun part—making the frosting! In a heavy-duty stand mixer, combine the chilled, browned butter and salt. Beat them together on medium speed until the mixture becomes creamy and well-blended. Gradually add the powdered sugar in batches, alternating with the reduced peach puree, vanilla extract, and whole milk. This technique helps to achieve a silky smooth Peach Buttercream Frosting. Continue to beat the mixture well after each addition until you reach your desired consistency; it should be light and fluffy with a beautiful peach color.