Preheat your oven to 350°F (175°C). Grease a regular loaf pan and set it aside.
Slice the zucchini. Do not squeeze out the moisture as it helps keep the bread moist.
In a large mixing bowl, combine the shredded zucchini, sliced green onions (if using), eggs, sour cream, and melted butter. Mix until well combined.
Fold in the shredded cheddar cheese, ensuring it is evenly distributed throughout the mixture.
In a separate bowl, mix the all-purpose flour, baking powder, baking soda, and salt together.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Be careful not to overmix.
Pour the batter into the greased loaf pan, smoothing the top. Bake in the preheated oven for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely. Slice and serve.