Preheat your oven to 350 degrees F. Butter a 9x5-inch loaf pan and dust it lightly with flour, tapping out the excess.

In a medium bowl, whisk together the whole wheat flour, baking soda, cinnamon, and salt until well combined.

In the bowl of a stand mixer fitted with the paddle attachment, beat the brown sugar, granulated sugar, eggs, coconut oil, and mashed bananas on medium speed for about 3 minutes, until smooth and well incorporated. Reduce speed to low and mix in the grated zucchini, grated carrots, sour cream, and vanilla extract until just combined.

Fold the flour mixture into the wet ingredients with a rubber spatula, stirring only until no streaks of flour remain. Gently fold in the chopped walnuts, scraping down the sides and bottom of the bowl.

Pour the batter into the prepared loaf pan and spread it evenly.

Bake on the middle rack for 50 to 55 minutes, or until a toothpick inserted into the center comes out clean. If the top browns too quickly, tent loosely with foil after 40 minutes.

Remove the pan from the oven and place it on a wire rack. Let the bread cool in the pan for about 10 minutes, then turn it out onto the rack to cool completely before slicing.