Preheat oven to 350 degrees F. Grate zucchini into a towel and squeeze to drain. Sprinkle with a few pinches of salt and allow zucchini to sit for 10-15 minutes. Squeeze to drain once more and set aside.
In a large bowl, whisk together eggs, brown sugar, sugar, vanilla extract, sour cream, and coconut oil. Add milk and whisk until smooth.
In a separate bowl, whisk together flour, baking soda, salt, cinnamon, nutmeg, and walnuts. Fold dry ingredients into wet ingredients. Then add in grated zucchini and fold into batter.
Spray a 9 x 5 loaf pan with oil and add batter. Sprinkle with coarse sugar and bake for 55-65 minutes, until a toothpick comes out clean.
Once the bread is finished baking, make the maple glaze. Heat butter in a small saucepan over low heat and add maple syrup. Whisk in confectioners sugar and remove from heat. Pour on top of zucchini bread.