Set out a medium heatproof bowl or glass liquid measuring cup because you’ll need it at the end of this step. Place the sliced butter in a light-colored skillet or saucepan. A light-colored interior allows you to determine when the butter begins to brown. Melt the butter over medium heat, stirring or whisking constantly. Once melted, the butter will begin to foam. Continue stirring/whisking, keeping a close eye on it. After about 5–7 minutes, the butter will begin browning and you’ll notice lightly browned specks forming at the bottom of the pan. The butter will have a nutty aroma. The color will gradually deepen, from yellow to golden to golden-brown; once it’s a light caramel-brown color, immediately remove from heat and pour into the bowl; be sure to scrape out and include the brown solids that have formed on the bottom of the pan. Cool for 10 minutes at room temperature, then transfer to the refrigerator to cool completely and solidify.

In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the solidified brown butter on high speed until creamy and smooth, about 1 minute. Add the cream cheese and beat again until smooth and combined, about 2 minutes. Scrape down the sides and bottom of the bowl as needed. Add confectioners’ sugar, vanilla, and salt. Beat on low speed for 30 seconds, then gradually increase to high speed and beat for 2 minutes.

Spread the frosting on cooled cake or cupcakes. If you plan to pipe the frosting, transfer it to a piping bag fitted with a piping tip and refrigerate it for 20–30 minutes before piping.

Cover leftover frosting tightly and store in the refrigerator for up to 1 week.