Pre-heat oven to 350 degrees. Grease and flour an 8x4 inch loaf pan. You can also line your pan with parchment paper if you prefer, this is what I like to do.
In a large bowl, mix egg, sugars, vanilla, and butter until well combined, then add all of your dry ingredients. The batter will be very dry.
Next, add your shredded zucchini. If your zucchini yields a bit more than 1 cup you can add up to about 1/4 cup extra but no more.
Mix for about 1-2 minutes to release the moisture from the zucchini. This will prevent your bread from being too dry. Pour into the prepared pan, the batter will be thick.
Bake for 45-50 minutes or until a toothpick inserted in the center comes out clean. Cool in the pan on a wire rack for 10 minutes then remove from pan. Cool completely on a wire rack before slicing and serving.