Preheat the oven to 350°F. Lightly grease a mini muffin pan with nonstick cooking spray.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In a separate large bowl, whisk together the granulated sugar, brown sugar, eggs, vegetable oil, melted butter, sour cream, and vanilla until smooth.
Add the dry ingredients to the wet ingredients and stir just until combined. Do not overmix.
Fold in the finely chopped or shredded zucchini until evenly incorporated.
Transfer the batter to a disposable piping bag (or a zip-top bag with the corner snipped off) and pipe the batter into the prepared mini muffin pan, filling each cup about ¾ full.
Bake for 10 to 13 minutes, or until the tops spring back lightly and a toothpick inserted into the center comes out clean.
Let the muffins cool in the pan for about 3 minutes, then carefully transfer them to a cooling rack.
In a medium bowl, stir together the granulated sugar and cinnamon.
While the muffins are still warm, gently toss a few at a time in the cinnamon sugar until lightly coated. Because these muffins are very tender, there's no need to coat them with butter first—the warmth of the muffins helps the cinnamon sugar stick beautifully.
Serve warm or allow them to cool completely before storing.