Brown the butter: Melt the butter in a skillet or small saucepan over medium heat. Swirl or stir the butter with a wooden spoon as it starts to foam and sputter. Remove the butter from the heat as soon as it begins to turn golden brown and smells nutty, about 1 minute. Strain through a fine sieve or coffee filter and let cool to room temperature.
Meanwhile, place the confectioners' sugar, milk, and corn syrup in the bowl of an electric mixer fitted with a whisk. Beat to combine.
With the mixer on medium, drizzle in the brown butter a little at a time, waiting until it is absorbed before adding more. Beat in another teaspoon of milk to make the frosting creamier, if necessary. Use on cakes, cupcakes, or cookies.
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