Preheat oven to 350°F. Spray a 9×5-inch loaf pan with floured cooking spray or grease and flour thoroughly. Set aside.
In a large bowl, whisk together brown sugar, oil, granulated sugar, sour cream, vanilla, and egg until smooth and well combined.
Add 1 cup flour, baking powder, baking soda, and salt. Stir just until combined, being careful not to overmix. Fold in the grated zucchini.
In a separate medium bowl, toss blueberries with the remaining ¼ cup flour until coated. Gently fold the floured blueberries and any loose flour bits into the batter.
Turn batter into prepared pan, smoothing the top lightly with a spatula. Sprinkle 1-2 tablespoons extra blueberries on top if desired.
Bake for 55-60 minutes until top is golden, center is set, and a toothpick inserted in center comes out clean or with a few moist crumbs (no wet batter).
Cool in pan for 20 minutes, then turn out onto a wire rack to cool completely before slicing.