Preheat the oven to 350 degrees and line a loaf pan with parchment paper. Spray the uncovered sides of the pan with non-stick cooking spray, or grease with oil.
In a mixing bowl, beat together the banana, eggs, sugar, oil and vinegar. Beat until smooth.
Add the dry ingredients (minus the nuts if using) and stir until a smooth batter forms. Fold in the nuts. Allow batter to rest for 5 minutes.
Transfer the batter to the prepared pan and bake in the center of the oven for 45 - 50 minutes, until a cake tester inserted into the center comes out clean. Check at 40 minutes and cover with tinfoil if the top is browning too quickly.
Cool in the pan for 5 minutes, then transfer to a wire rack and cool completely before slicing.
Serve slightly reheated in the toaster oven with your favorite nut butter or buttery spread