Melt the butter in a large skillet over medium-low heat, swirling occasionally, until the milk solids in the butter have turned golden brown and the butter smells toasty, about 10 minutes. Pour the butter into a shallow baking dish, and refrigerate until it is solid but still soft enough that your finger leaves an indentation, about 25 minutes.
Scrape the cooled butter into a large bowl (be sure not to leave any brown bits in the skillet), and beat with an electric mixer on medium-high speed until smooth. While continuing to beat, add the corn syrup, and beat until incorporated. Scrape down the side of the bowl. Adjust the speed to medium-low, add the confectioners' sugar and salt, and beat until smooth. Use right away or keep for up to 2 hours at room temperature in an airtight container.
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