Preheat oven to 375° F. Line a muffin pan with muffin liners and set aside.
In a medium bowl, mix together vegetable oil, eggs, granulated sugar, brown sugar and vanilla until well combined. Set aside.
In a large bowl, whisk together flour, baking soda, baking powder, salt and cinnamon. Add wet ingredients to the dry ingredients and stir until combined (be careful not to over mix). Add shredded zucchini and carrot, and stir until incorporated.
Use a spoon (or an ice cream scoop I find using this you get a more exact measurement for each muffin) to transfer batter into prepared muffin pan until each cup is about three-quarters full. Whisk together cinnamon sugar topping and sprinkle on top of muffins. Bake at 375° F for 20 minutes, or until a toothpick inserted in the center of a muffin comes out with little to no crumbs.
Cool muffins in the pan for 3 minutes then remove muffins to a wire cooling rack. Serve warm or at room temperature. Store in an air tight container at room temperature for up to 5 days.