Preheat oven to 350 degrees F. Spray the insides of an 8x4-inch loaf pan and then line it with parchment paper; letting the paper hang over the sides.
Whisk together the flour, baking soda and salt in a large bowl and set aside.
In a medium mixing bowl, whisk together the eggs, banana, sugars, buttermilk, oil, peanut butter and vanilla extract until smooth.
Combine the wet ingredients in the large bowl with the flour mixture and fold together with a spatula until completely combined. Fold in the milk chocolate chips.
Transfer the batter to the prepared loaf pan, smoothing the top. Bake until the loaf is golden brown and a toothpick inserted into the center comes out with just a few moist crumbs, 60 - 75 minutes. Check at 45 minutes and cover the bread with aluminum foil if the top is adequately browned.
Allow the bread to cool in the pan for about 10 minutes, then turn it out onto a wire rack to cool completely. Wrap the bread in plastic wrap to keep and store at room temperature for up to 5 days. We love it toasted a bit!