Preheat the oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or grease it lightly with olive oil.
In a large mixing bowl, combine the shredded zucchini, grated carrot, chopped red bell pepper, and chopped red onion.
In a separate bowl, whisk together the chickpea flour, rolled oats, baking powder, baking soda, salt, black pepper, garlic powder, and smoked paprika.
In another bowl, beat the eggs, then add the Greek yogurt, olive oil, and grated Parmesan cheese. Mix well.
Add the wet ingredients to the dry ingredients and stir until just combined.
Fold in the chopped fresh parsley and the mixed vegetables until evenly distributed.
Spoon the batter evenly into the prepared muffin tin cups, filling each about 3/4 full.
Bake for 22 to 25 minutes, or until the muffins are golden brown and a toothpick inserted into the center comes out clean.
Remove from the oven and let the muffins cool in the tin for 5 minutes before transferring them to a wire rack to cool completely.