Roasted Banana Cupcakes with Browned Butter Frosting

This was originally a cake recipe, but I thought it would be fun to make cupcakes instead and change the frosting a little.

Cake:
2 C. sliced ripe bananas
1/3 C. packed dark brown sugar
1 T. butter, chilled and cut into small pieces
2 1/4 C. flour
3/4 t. baking soda
1/2 t. baking powder
1/4 C. buttermilk
1 t. vanilla extract
1/2 C. butter, softened
1 1/4 C. granulated sugar
2 large eggs

Preheat oven to 400 F. Combine banana, brown sugar, and 1 T. butter in a baking dish (8-inch is good). Bake for 35 minutes, stirring after 17 minutes. Cool slightly and mash. Reduce oven temperature to 350 F. Combine 2 1/4 C. flour, soda, and baking powder in a medium bowl. Combine banana mixture, buttermilk, and 1 t. vanilla in a separate bowl. Place 1/2 C. butter and granulated sugar in a large bowl; beat with a mixer at medium speed until well blended. add eggs; mix well. Add flour mixture to sugar mixture alternating with banana mixture, beginning and ending with flour mixture.
Place a cupcake liner in each cupcake tin and fill half way with batter. You should get about 24 cupcakes. Bake for 15 to 20 minutes or until tooth pick comes out clean. Do not overbake. Cool on a wire rack.

Frosting:
1/2 C. butter
6 oz. cream cheese, room temperature
2 C. powdered sugar
1/4 t. vanilla extract
Melt butter in a small saucepan over medium heat; cook for about 4 minutes, or until lightly browned. Remove from heat and pour into a medium sized glass bowl. Place the browned butter in the refrigerator until it is just barley solidified and about room temperature. This will take about 15 minutes, give or take a few minutes. Remove from the fridge and add the cream cheese. Beat until fluffy, about 5 minutes. Add the powdered sugar and vanilla and beat until smooth and fluffy. Let the frosting chill in the fridge for about 1 hour before frosting the cupcakes.