Preheat your oven to 375°F (190°C). Grease a 12-cup muffin tin or line with paper liners.
In a large bowl, combine the grated zucchini and shredded cheddar cheese.
In another bowl, whisk together the flour, baking powder, baking soda, and salt.
In a separate bowl, beat the eggs, then add the vegetable oil and milk. Mix well.
Add the wet ingredients to the dry ingredients and stir until just combined. Do not overmix.
Fold in the zucchini and cheddar mixture.
Spoon the batter into the prepared muffin tin, filling each cup about ¾ full.
Bake for 20-25 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Let the muffins cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.