Preheat oven to 350 degrees F and line a muffin pan with cupcake liners.

In a large mixing bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.

In another large mixing bowl, whisk together the granulated sugar and eggs for about 2 minutes, until well combined and slightly lightened in color. Add the mashed bananas, vegetable oil, and vanilla and mix until just combined.

Alternate adding the flour mixture and the buttermilk, mixing well between each addition, until all ingredients are incorporated and the batter is smooth. Stir in the vanilla extract.

Fill each cupcake liner 2/3 full of batter. Bake for 18–20 minutes, until a toothpick inserted into the center comes out clean. Transfer cupcakes to a wire rack to cool completely.

Meanwhile, add the butter to a large skillet and heat over medium heat. Allow the butter to melt, then simmer and foam, stirring constantly. Continue cooking as the foam subsides and the milk solids sink and turn golden brown, about 5–8 minutes. The butter should be amber in color with a nutty aroma.

Remove from heat and immediately pour into a heatproof bowl. Cover and chill for about 1 hour, until cooled and beginning to solidify.

Beat the cooled browned butter on medium speed with an electric mixer until fluffy.

Gradually add the powdered sugar, alternating with the heavy whipping cream, until incorporated. Mix for 2-3 minutes until smooth and creamy. (Be sure not to over-mix, as the heavy whipping cream will start to curdle and separate.)

Transfer the frosting to a piping bag fitted with a Wilton 1M tip and frost the cooled cupcakes.