Place shredded carrots, steamed broccoli, garlic, eggs, 1 cup of the breadcrumbs, cheese, onion powder, and black pepper in a food processor and pulse until well combined.
Form mixture into 25 nugget sized balls. Coat each veggie nugget with breadcrumbs.
Heat oil in a pan on medium heat.
Arrange nuggets in pan and cook 4 minutes each side, or until golden brown and crisp.