Melt one tablespoon of butter in a small saucepan over medium heat until it crackles, then turns a dark brown. It should begin to smell nutty and generally awesome. I didn’t let the butter go as dark as I did for these apple crumbles, since I figured the flavor would be stronger in frosting, but the darker the butter is, the stronger the brown butter flavor will be. Set aside and let cool.
If mixing by hand like I did, cream butter and cheese together until very smooth. Add salt and 1/2 cup of powdered sugar, then beat again until incorporated. Add the remaining powdered sugar in two batches, beating after each addition. Finally, add maple syrup and beat again until smooth.
If the frosting is too runny, add more confectioners’ sugar, a few tablespoons at a time, until it reaches the desired consistency. Alternatively, you can let it chill in the refrigerator for 15-30 minutes before spreading to increase its firmness. I only used 1/2 tablespoon of maple syrup, so I found it to be the right consistency to spread right away.