Preheat an oven to 180c (350f) and prep a 9x5 inch loaf pan with parchment paper. In a box grater, on the smaller holes (to get finely grated zucchini) great the zucchini with the peel on. Take a handful at a time and squeeze out excess liquids.
In a large mixing bowl, add the eggs, brown sugar, sugar, oil, vanilla extract, melted and cooled butter, yogurt, kosher salt, cinnamon, and nutmeg, and, mix with a whisk until well combined.
Add the shredded zucchini and mix with a whisk until combined.
Add the flour, baking powder, and baking soda, and mix until almost combined.
Add the chocolate chips and fold the mixture using a spatula until the mixture is just combined. Do not overmix the batter, so it won't develop gluten and turn dry.
Pour the batter into a parchment paper-lined loaf pan and top the batter with extra chocolate chips. Bake in a 180c (350f) preheated oven for 50-60 minutes or until a toothpick inserted into the bread comes out clean.
Let the bread cool for at least 30 minutes before serving.