While the cupcakes are baking, scrape the room temperature cream cheese into the bowl of your stand mixer and use the paddle attachment to slowly beat the cheese until it's completely smooth. Be sure to scrape down the sides of the bowl. This shouldn't take more than 5 minutes with room temperature cream cheese. While you're doing this, pull your brown butter out of the fridge so it can warm up a bit. You want it to remain firm but not be super cold or it will be hard to incorporate into the buttercream.
Make sure your caramelized white chocolate is still liquid. If it isn't, put it in the microwave and nuke for 10 second intervals, stirring each time, just until it's completely melted.
With the mixer on low, slowly drizzle the chocolate into the cream cheese. Once it's all in, turn off the mixer, scrape down the bowl, and then turn the mixer to medium and whip until creamy and homogenous.
With the mixer on low again, begin adding the brown butter, spoonful by spoonful. Make sure to add all those yummy brown bits! (Melted and re-solidified butter has a weird texture, don't be concerned, it's main use is for flavor at this point, not creaminess. The cream cheese will supply all the creaminess that you need.)
Once the mixture is fluffy and well incorporated, add your vanilla. You may want to add a pinch of salt as well, totally up to you!
This is a lovely buttercream for piping on cupcakes, it's so smooth and creamy and creates perfect mounds of frosting. I like to use a plain tip to keep the cupcakes simple and rustic but a star tip would work just as well.
I also added some candied carrot slices for color. These are very simple to make: Heat 1 cup sugar and 1 cup water in a small saucepan until the sugar is dissolved and the resulting syrup is simmering. Add 1/4 cup of thinly sliced carrot slices to the syrup and allow them to simmer for 30 minutes. Drain the slices and dry in one layer on a sheet pan. You'll notice the edges of the carrots will start to ruffle as they dry, and resemble little flowers. Save the leftover carrot syrup to sweeten your next cocktail!