Preheat oven to 350F. Coat the sides and base of an 8 inch springform pan. Dust with flour.
In a large bowl, combine browned butter, sugar, bananas, eggs and vanilla. Beat on medium high for 2 minutes. Add buttermilk and mix until combined.
In a separate bowl, combine flour, baking powder, salt and baking soda. Add into the banana mixture. Beat until just combined.
Pour batter into prepared pan. Place into oven and bake for 50-60 minutes or until a toothpick comes out clean. Leave to cool on a wire rack for about 10 minutes. Run a knife around the edge if needed and remove the sides of the springform pan. Once cool enough, remove the springform bottom and transfer to a cooling rack to cool completely.
For the ganache
In the microwave, combine the chopped chocolate and heavy cream. Microwave for 45 seconds. Stir. Microwave in 10 seconds increments, stirring in between, until the chocolate is completely melted and the mixture is smooth and glossy. Let cool slightly (about 5 minutes) and pour over the cooled cake.