Preheat oven to 350 degrees. Grease and flour a bundt pan.
Add cake mix, applesauce, melted butter, milk, and eggs to the bowl of a mixer and beat until well combined, about 2 minutes.
Pour batter into prepared bundt pan and bake for 35-40 minutes or until a toothpick inserted in the center comes out clean.
Let cake cool for 10 minutes in the pan before flipping onto a cake plate. Cool completely before glazing.
To prepare the glaze, melt the butter in a small sauce pan over medium heat. Once butter begins to foam, whisk constantly so that you can see the color of the butter underneath the foam. Continue cooking until butter begins to turn a deep golden brown.
Remove from the heat and whisk in the powdered sugar until smooth.
Drizzle the glaze over the top of the cake.
Let sit for 15 minutes for the glaze to firm up before serving.
Store in the refrigerator, tightly covered, for up to 3 days.