Preheat oven to 350°F and lightly grease muffin tin with canola oil (take from 1/3 cup used in recipe).
Grate zucchini and gently squeeze out some excess moisture using paper towel or a clean kitchen towel. Do not completely dry it out as some moisture helps keep the muffins soft.
In a large bowl, whisk together flour, sugars, baking soda, baking powder, cinnamon, and salt.
In a separate smaller bowl, whisk eggs, oil, vanilla, and Greek yogurt until smooth.
Add the wet ingredients to dry ingredients and stir until just combined.
Fold in the grated zucchini and walnuts.
Divide batter evenly between muffin cups, filling each about three-quarters full.
Bake for 20 to 24 minutes, or until a toothpick inserted into the centre comes out clean.
Allow muffins to cool in the pan for 5 minutes before transferring to a wire rack.