Preheat the oven to 350°F (180°C).
Butter or spray 12 regular muffin tins or line with paper cups.
In a large bowl, beat ¾ cup oil with ½ cup brown sugar and ½ cup white sugar for 1 minute.
Add 2 eggs one by one, beating until fully incorporated, but don’t overbeat.
Add 6 tablespoons pumpkin puree and ½ teaspoon vanilla, and mix well.
Sift 2 cups flour, 1 and ½ teaspoons baking powder, ½ teaspoon baking soda, ½ teaspoon salt and ½ teaspoon cinnamon.
Add to the pumpkin mixture in 2 parts, integrating well with a spatula or whisk. I don't recommend an electric mixer so as not to overmix them.
Add 1 cup grated zucchini and stir with a spatula.
Fill the paper liners up to ¾ of their capacity. Do not fill more than that, so they don’t overflow while baking.
Bake for about 25 minutes, until a cake tester or toothpick comes out dry.
Let cool on a wire rack.
Store covered at room temperature for two days and then refrigerate or freeze, covered or well wrapped. Warm lightly in the oven before eating.