Preheat oven to 350°F. Grease two 8x4-inch loaf pans or line with parchment paper.
In a large bowl, beat the eggs. Add the avocado oil, sugar, grated zucchini, and vanilla extract, mixing well.
In a medium bowl, whisk together the gluten-free flour, baking soda, cinnamon, and salt.
Add the dry ingredients to the wet ingredients and stir until just combined. Do not overmix.
Divide the batter evenly between the prepared loaf pans.
Bake for 60–70 minutes, or until a toothpick inserted into the center comes out clean.
Cool in the pans for 5 minutes, then remove and cool completely on a wire rack.