Preheat your oven to 200°C (390°F) and line a baking sheet with parchment paper or a silicone mat.
Finely grate or pulse the cauliflower florets and carrots until they resemble small crumbs or rice-sized pieces. This creates a uniform, tender base for the nuggets.
In a large mixing bowl, combine the grated vegetables with the breadcrumbs, grated cheese, paprika, garlic powder, and beaten egg. Mix everything together until well integrated and the mixture feels cohesive.
Using your hands or an ice cream scoop, shape the mixture into small nuggets about 2 inches long and 1 inch wide. Press gently to compact them, ensuring they hold together well.
Arrange the shaped nuggets on the prepared baking sheet, spacing them evenly. Brush the tops lightly with olive oil using a pastry brush for a golden, crispy finish.
Bake the nuggets in the preheated oven for 20 to 25 minutes, flipping them halfway through for even browning. They should turn a deep golden brown and develop crispy edges.
Remove the nuggets from the oven and let them rest for 5 minutes on the baking sheet. This helps them set and prevents them from falling apart when served.
Serve the veggie nuggets warm, with your favorite dipping sauce or as a side. They should be crispy on the outside and tender inside, with a flavorful vegetable taste.