Light and moist, this coffeecake-style treat makes a nice change from muffins. For the best flavor, make sure your bananas are very ripe and toast the nuts before adding them to the batter.
Position a rack in the lower third of the oven and preheat to 325 degrees F. Butter a 9x13-inch baking pan heavily and set aside.
In the bowl of a mixer, beat the butter with the brown sugar until smooth. Beat in two egg yolks (reserve the whites). On slow speed, add the mashed banana, vanilla, and sour cream.
In a separate bowl, whisk the flour, salt, and baking soda to combine. Add to the batter, mixing slowly to just combine; don't overmix. Stir in the nuts.
In a clean bowl, beat the egg whites until they form stiff (but not dry) peaks. Add half of the beaten whites to the cake batter and stir gently to lighten. Fold in the remaining whites.
Transfer the cake batter to the prepared pan and spread evenly. There isn't a lot of batter for the size of the pan.
Bake until a toothpick inserted into the center of the cake comes out clean and the edges of the cake have pulled away from the pan, 40 to 50 minutes. Let cool for 10 minutes before cutting into squares.