Preheat oven to 350 degrees. Grease a baking pan and set aside.
Add the onion and garlic clove to a food processor and pulse until almost pureed. Add carrots, broccoli florets, cheddar cheese, eggs, salt and pepper, and 1 1/4 cups breadcrumbs and pulse until everything is incorporated. Set aside.
In a small bowl combine the remaining breadcrumbs with the paprika and some salt and pepper.
With the help of spoon shape each nugget. Press firmly into the breadcrumbs so they get completely coated.
Transfer to a baking pan. Brush all the nuggets with the oil and take to the oven.
Bake for 15 minutes or until golden.