Preheat oven to 350 degrees
Melt one stick of butter and let it cool while you prepare the other ingredients.
Spray every inch of your bundt pan with non-stick spray.
Measure out one cup of white chocolate chips and finely chop. You can also use a food processor to speed up the process. Process until they are tiny crumbles.
To a bowl or stand mixer with the whisk attachment add the box cake mix and the box pudding mix. Whisk until combined.
To another bowl add buttermilk, four eggs, vanilla, and your cooled melted butter. Whisk.
With the mixer on low add the wet ingredients into the dry. Slowly increase speed until you're on high. Allow the batter to get beaten on high for 1 full minute. Scrape the bowl down and beat until everything is incorporated.
Fold in the white chocolate.
Pour into your prepared bundt pan and evenly spread out.
Bake for 40-43 minutes. If your oven cooks faster or is small (double oven) check with a toothpick at 35 minutes. If it comes out without batter on it, it's done.
Remove the cake from the oven and let it cool completely in the bundt pan to room temperature. This should take hours.
Once the cake is done cooling prepare your icing. To a pan melt the butter over medium heat. It will sizzle and bubble for a few minutes. It will turn golden and then right when it starts to go from golden to an amber color, pull it off the heat and swirl it around. It will continue to darken. If it burns and goes black, start over.
Set the butter aside to cool for a few minutes.
To a bowl or a stand mixer fitted with the whisk attachment add your powdered sugar. Add the melted brown butter, milk, vanilla and salt. Whisk until fully incorporated.
Immediately spread on top of the cooled cake. Scrape excess icing off the cake to expose the some of the cake underneath. You want it to be lightly iced. This is called a "naked cake."
Let the icing set for 30 minutes then slice and enjoy.