Preheat the oven to 180°C (350°F) and position the wire rack in the center.
Grease all the inside surfaces of a loaf pan with butter and set it aside.
Wash and thoroughly dry the zucchini, then cut off the stem end. Grate the zucchini using the coarse side of a box grater.
Squeeze out as much moisture as possible from the grated zucchini by pressing handfuls between your palms. After squeezing, you should have about 1 cup of grated zucchini.
In a bowl, whisk together the flour, salt, black pepper, and baking powder until well combined.
In a separate large bowl, whisk the eggs, milk, and olive oil together. Stir in the grated zucchini, ensuring it is evenly distributed.
Add the dry ingredients to the wet ingredients and fold together gently with a spatula until no streaks of flour remain.
Fold in the grated cheddar cheese and chopped green onions carefully, mixing just until evenly combined without overmixing.
Pour the batter into the prepared loaf pan and smooth the top with the back of a spoon or an offset spatula.
Bake for 50 minutes, or until a toothpick inserted into the center comes out clean.
Allow the loaf to cool in the pan on a wire rack for 10 minutes, then run a knife around the edges to loosen it. Remove the bread from the pan and let it cool completely on the rack.
Once fully cooled, slice the cheesy zucchini bread and enjoy.