Preheat the oven to 350F and spray a 9x5-inch loaf pan with gluten-free nonstick cooking spray, then line with parchment paper.
In a large bowl, whisk together the gluten-free flour blend, xanthan gum, baking powder, baking soda, salt, and cinnamon. Set aside.
In a medium bowl, whisk together the eggs, brown sugar, coconut milk, oil, and vanilla extract.
Pour the wet ingredients into the dry ingredients. Mix until just combined, then fold in the grated zucchini.
Transfer the batter to the prepared baking pan. Bake for 50-60 minutes or until a cake tester or toothpick comes out clean. Cool in the pan for 20 minutes then remove the bread from the pan, remove the parchment paper, and cool on a wire rack.
Keep the bread wrapped tightly in plastic wrap at room temperature for up to 3 days. To freeze, wrap tightly in plastic wrap then freeze in a freezer-safe bag for up to 3 months.
*There’s no need to take the extra step of squeezing out any extra liquid from the zucchini. This recipe relies on that moisture.