Shred carrots, and steam broccoli in the microwave for two minutes or until tender.
Place shredded carrots, steamed broccoli, garlic, eggs, 1 cup of the breadcrumbs, cheese, onion powder, and black pepper in food processor and pulse for 15 seconds or until well combined. Mixture should form easily into a ball. If it's too crumbly, add water one teaspoon at a time until you achieve the desired consistency.
Form mixture into balls, about a tablespoon each (I use a cookie scoop). You should get about 25 nuggets. Flatten slightly into round discs about ½-inch thick.
Place remaining ¼ cup breadcrumbs in a shallow dish. Coat each veggie nuggets with breadcrumbs.
Heat oil in a skillet on medium high heat until it sizzles when sprinkled with water droplets.
Arrange nuggets in skillet and cook about 4 minutes each side, or until golden brown and crispy.
Serve with honey-mustard sauce, ketchup, or other favourite dip.