Start by melting the butter in a medium saucepan over medium heat. Keep a close eye as it melts; it will begin to foam and then turn a golden brown with a nutty aroma. This usually takes about 5-7 minutes. Remove from heat immediately once browned to avoid burning, and transfer to a heatproof bowl to cool slightly.
While the butter cools, shred your zucchini using a box grater. Place the shredded zucchini in a clean kitchen towel and squeeze out as much moisture as possible. Rinse and gently pat dry the fresh blueberries. Toss the berries with a tablespoon of flour to help keep them suspended in the batter evenly.
In a large bowl, whisk together the granulated sugar and browned butter until combined. Add the eggs one at a time, whisking well after each addition. Mix in the vanilla extract. The mixture should be smooth and slightly glossy.
In a separate bowl, sift together the all-purpose flour, baking soda, baking powder, salt, and ground cinnamon.
Gradually add the dry ingredients to the wet mixture, folding gently with a spatula until just combined. Avoid overmixing to keep the bread tender. Next, fold in the shredded zucchini, flour-coated blueberries, and chopped walnuts if using. The batter should be thick but moist.
Preheat your oven to 350°F (175°C). Grease a standard 9x5-inch loaf pan and pour in the batter, smoothing the top with a spatula. Bake for 55-65 minutes, or until a toothpick inserted in the center comes out clean or with just a few moist crumbs. If the top browns too quickly, tent with foil halfway through baking.
Allow the loaf to cool in the pan for about 15 minutes before transferring it to a wire rack to cool completely. Serve plain, or with a smear of butter or cream cheese for extra indulgence.