Preheat the oven to 350°F (175°C). Coat a 9 x 5-inch loaf pan with non-stick cooking spray.
Wrap the shredded zucchini in a paper towel and press it gently to remove some of the extra liquid. The zucchini should remain moist, but roughly one tablespoon of liquid should be released.
In a large mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until the leavening agents and seasoning are evenly dispersed.
In a separate small bowl, stir the milk and vinegar together. Let the mixture rest briefly until the milk begins to curdle slightly, forming a quick buttermilk-style base.
Whisk the melted butter and egg into the milk mixture until the liquid ingredients are smooth and fully combined.
Pour the wet mixture into the bowl with the dry ingredients. Fold gently until just incorporated, taking care not to overmix, as excessive stirring can make the loaf dense and prevent it from rising properly.
Add the prepared zucchini, grated sharp cheddar, and chopped green onions to the batter. Fold only until the add-ins are evenly distributed throughout the mixture.
Transfer the batter into the prepared loaf pan and smooth the surface evenly.
Bake for about 1 hour, or until a toothpick inserted into the center of the loaf comes out clean.
Allow the bread to rest in the pan for 10 minutes. Carefully remove it from the pan and place it on a wire rack to cool completely before slicing.