Pumpkin Applesauce Muffins with Apple Frosting

I found a pumpkin- applesauce bundt cake  recipe and made muffins out of it since I couldn't find my bundt cake pan. It calls for gluten free flour, and that is what I used, but I don't see why any ol' all purpose flour wouldn't work. I baked the muffins at 350 degrees for 21 minutes, and I replaced half the cinnamon with pumpkin pie spice. Delicious! But, I really wanted to highlight the apple so I whipped up some apple frosting:

1/4 cup butter (at room temperature)
1/2 teaspoon vanilla
Enough powdered sugar to reach desired thickness
1 finely chopped apple
Garnish with cinnamon