Heat the oven to 375 degrees. Line a mini muffin tin (or standard size muffin tin) with paper liners or grease well.
Grate the zucchini on the smaller holes of a box grater until you have 1 1/2 cups of grated zucchini. Place the zucchini into a clean kitchen towel and squeeze out all of the excess moisture. You should have a full cup of grated zucchini after the liquid is squeezed out.
In a large bowl combine the grated zucchini, cottage cheese, sugar, maple syrup, vanilla, oil, and milk.
Add the flour then sprinkle over the baking powder, baking soda, salt, and cinnamon. (You could also whisk the dry ingredients together in a separate bowl first if you prefer.) Stir with a large spoon or spatula until everything is just combined. The batter will be thick, but try not to overmix or the muffins with be dense or tough.
Scoop the batter into the muffin tin, filling each hole about 3/4 of the way. Press some mini chocolate chips into the top of some or all of the muffins, if you'd like.
Bake until lightly golden brown on the top, 12 to 14 minutes for mini muffins and 16 to 20 minutes for standard muffins. Allow to cool fully before enjoying.
Muffins can be stored at room temperature for 2 days or refrigerated for 5 days. To freeze, wrap well and freeze up to 2 months.