Preheat oven to 375. Prepare a 9x13 inch baking pan coating with oil and flour; set aside. In a medium bowl, whisk together the flour, baking soda and salt; set aside.
Using an electric mixer, beat the sugar and oil together until completely combined, then mash the bananas and vanilla extract until combined. Reduce the speed to low and add the flour mixture in three additions, alternating with the buttermilk, mixing until combined. Use a rubber spatula to give the batter one last mix, then pour into the prepared pan.
Bake for 30-35 minuthes until the top is golden brown or until a toothpick inserted into the center comes out clean. Set on a wire rack to cool.
For the frosting brown butter in a saucepan over medium heat until it is boiling and a delicate brown color appears. Remove from the heat and immediately add the remaining ingredients. This should be thicker than a glaze and thinner than frosting. Using a spatula smooth over the top of the cake while the cake is still warm.