Preheat oven to 400 F for muffins, mini loaves and mini Bundts or 375 F for a large loaf. Coat pan(s) with cooking spray.
Mix the dry ingredients in a large bowl.
Whisk eggs, buttermilk, brown sugar, butter, oil and vanilla in a large bowl until well combined.
Make a well in the center of the dry ingredients, pour in the wet ingredients and stir until just combined. Add banana, walnuts and chocolate chips. Stir just to combine; do not overmix. Transfer batter to the prepared pan(s). Top with additional walnuts, if desired.
Bake until golden brown and a wooden skewer inserted into the center comes out clean, 22 to 25 minutes for muffins or mini Bundts, 35 minutes for mini loaves, 1 hour 10 minutes for a large loaf. Let cool in the pan(s) for 10 minutes, then turn out onto a wire rack. Let muffins and mini Bundts cool for 5 minutes more, mini loaves for 30 minutes, large loaves for 40 minutes.
Store, individually wrapped, at room temperature for up to 2 days or in the freezer for up to 1 month.
Tip: To toast walnuts, spread nuts onto a baking sheet and bake at 350 F, stirring once, until fragrant, 7 to 9 minutes.