Several weeks or a day ahead, make the caramelized white chocolate: I don't think I can do better than the venerable Dave Lebovitz when it comes to explaining how to caramelize white chocolate so I am simply going to send you to his recipe here: https://www.davidlebovitz.com/caramelized-white-chocolate/ You'll see that he uses 12 oz instead of 16 oz chocolate but this doesn't matter. Just follow the directions and expect the process to take a bit longer. My advice is remember to use a high quality chocolate with a high cocoa butter content. Use a lower cocoa butter content and you run the risk of crumbly, chalky chocolate, as David mentions. Also, make sure to stir it every 10 minutes and keep the oven temperature to 250°F--this isn't a process to speed up! Just start this process first and continue to prepare your other ingredients in between stirring sessions. Lastly, if it's a bit lumpy and you need to smooth it out with the immersion blender or hand mixer, do it while the chocolate is still warm. It's much easier.
Once the chocolate is caramelized and smooth, allow it to cool, covered, on the counter, while you work on the cupcakes. You want it to still be liquid for the buttercream but not too warm or it will melt the cream cheese and butter.
A day or 3 hours ahead, make the brown butter: In a small saucepan, melt the 1/2 lb of butter over medium heat. The butter will sputter and foam. Keep a close eye on it. As it begins to brown, carefully stir it with a wooden spoon to scrape all the brown bits from the bottom of the pan. When the butter is a golden brown, remove it from heat. It will continue to cook and become a darker brown. Scrape the pan a few more times to make sure the brown bits don't stick to the bottom. Let the butter cool to room temperature, then scrape it into a plastic container, cover, and put in the fridge to solidify. (You will use this for your buttercream later.)
Make the buttercream: 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 the brown butter out of the fridge so it can warm up a bit. You want it to remain firm but not super cold or it will be hard to incorporate into the buttercream.
Bring your caramelized white chocolate back to a liquid state by nuking it in the microwave 20 second intervals, stirring and breaking it up 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! Use immediately on your cupcakes. The frosting can, of course, be refrigerated and re-whipped as needed.