Start by washing and roughly chopping the carrots and zucchini. Blanch the carrots in boiling water for 2 minutes, then drain and let cool slightly.
Place the chopped vegetables into a food processor and pulse until finely minced but not pureed. Transfer the mixture into a large mixing bowl.
Add bread crumbs, grated cheese (if using), beaten egg, garlic powder, paprika, and a pinch of salt to the bowl. Mix everything thoroughly with a spatula until well combined. The mixture should hold together when pressed; if too wet, sprinkle in more bread crumbs.
Shape the mixture into small nuggets, about 2 inches long and 1 inch wide, using your hands. Place each on the prepared baking sheet lined with parchment paper or a silicone mat.
Lightly brush or spray the nuggets with oil to help them crisp up during baking. Place the tray in a preheated oven at 200°C (390°F) and bake for 20 minutes, flipping halfway through, until the nuggets turn golden brown and crispy around the edges.
Once baked, remove the nuggets from the oven and let them rest for 5 minutes. They should be firm, crunchy on the outside, and tender inside. Serve warm with your favorite dip or a simple salad for a satisfying snack or meal.
