Preheat the oven to 350°F (180°C).
Have a 12-muffin tin lined with paper cups (paper liners) or buttered. Using liners is very convenient because you hardly have to wash the muffin tin, and the muffins are easier to transport if necessary.
Grate or shred 1 ½ cups grated zucchini and 1 ½ cups grated carrots (lightly packed) with a large-holed grater at the last moment when you have the rest of the ingredients ready so they don't release extra liquid. If watery, blot them with a paper towel to remove excess moisture before adding them.
Whisk together 2 eggs and 1 cup sugar in a large bowl.
Add ¾ cup oil in a thin stream as you continue whisking. Incorporate it well, but there's no need to beat much.
Add the sifted dry ingredients (2 cups all-purpose flour, 2 teaspoons baking powder, ¾ teaspoon baking soda, ¼ teaspoon salt and ¼ teaspoon ground cinnamon) and stir a little. It doesn't need to be fully incorporated before you add the rest of the ingredients. Change to a spatula for easier folding. You can have the ingredients measured and sift them directly over the oil batter (like I do) or sift them in a medium bowl first and then add them to the muffin batter. Fold in the grated carrots and zucchini. You will see that the moisture in the vegetables loosens up the batter. You mustn't over-mix or beat the dough after adding the flour to keep the muffins as soft and fluffy as possible.
Scoop portions into the paper liners dividing as evenly as possible.
Bake for about 20 minutes, until golden brown, domed, and a cake tester or toothpick inserted in the center comes out clean.
Let cool on a wire rack (cooling rack).
Store at room temperature for two days and then refrigerate or freeze, always well wrapped.