Preheat the oven to 350 degrees Fahrenheit. Spray a 9 x 5 inch loaf pan with nonstick cooking spray.
In a large bowl. combine the sugar, brown sugar, mashed banana, and vegetable oil. Mix well with a spatula.
Add the eggs and mix until incorporated.
Add the all-purpose flour, baking powder, baking soda, and kosher salt to the bowl. Stir until a smooth batter forms, and the dry ingredients are completely incorporated.
Pour the batter into the greased loaf pan. Bake for 40 to 45 minutes, or until a toothpick comes out clean.
Let the banana bread cool for a few minutes before flipping it onto a wire rack.
In a small bowl, whisk the powdered sugar, water, and vanilla. While the banana bread is still slightly warm, generously drizzle the icing onto the top of the banana bread until completely covered.