Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
Grate the carrot and zucchini. Make sure to squeeze out the excess water from the grated zucchini using a clean towel or paper towels, as this will help the nuggets hold their shape.
In a food processor, blend the chickpeas until they are broken down but still slightly chunky. Transfer the chickpeas to a mixing bowl, and add the grated carrot, zucchini, gluten-free oats or oat flour, ground flaxseed, nutritional yeast (if using), garlic powder, onion powder, salt, and pepper. Mix everything together until well combined and a dough forms.
Using your hands, scoop out small portions of the mixture and shape them into nugget-sized patties. Place them on the prepared baking sheet, making sure they are evenly spaced.
Bake the nuggets in the preheated oven for 20-25 minutes, flipping them halfway through, until they are golden brown and slightly crispy on the outside.
Let the nuggets cool slightly before serving. Enjoy them with your favorite dipping sauce like ketchup, hummus, or tahini sauce.