Preheat oven to 350 degrees Fahrenheit.
Heat butter in a small saucepan over medium heat for 2 to 4 minutes, or until browned.
In a large bowl, combine the browned butter, banana, and granulated sugar; beat on medium speed until smooth. Add the eggs one at a time; beat well after each addition. Beat in the vanilla extract.
Measure flour by fluffing it with a fork then lightly spoon it into a dry measuring cup, level the top with the back of a knife. Combine the flour, baking powder, baking soda, salt, and cinnamon in a medium bowl; stir with a fork or whisk. Gradually add the flour mixture to the banana mixture alternating with the milk. Begin and end with the flour mixture.
Line a 12 cup muffin pan with paper cups. Spoon ¼ cup of batter into each cup. Bake for 20 to 24 minutes or until the cupcake springs back when touched. Remove from pan immediately and allow the cupcakes to cool completely on a wire rack.
To make the frosting: Beat the butter on medium speed until fluffy. Add the powdered sugar; beat on low until smooth. Beat in vanilla extract and heavy cream just until incorporated. Fold in toffee bits. Spread the frosting over the cupcakes and top with additional toffee bits if desired.