Preheat your oven to 200°C (390°F). Line a baking sheet with parchment paper or a silicone mat to prevent sticking and ensure even baking.
Finely grate the carrots and zucchini using a box grater or food processor. Transfer the grated vegetables to a clean kitchen towel and squeeze out as much moisture as possible—that step is key to helping the nuggets hold together during baking.
In a large mixing bowl, combine the drained vegetables with the breadcrumbs, shredded cheese, beaten egg, smoked paprika, salt, and a drizzle of olive oil. Mix everything until well combined and sticky enough to shape into small nuggets.
Shape the mixture into about 2-inch long and 1-inch wide nuggets. Place them on the prepared baking sheet, spacing them apart to allow for even crisping.
Lightly brush or spray the tops of the nuggets with olive oil. This helps them develop a golden, crispy exterior in the oven.
Bake the nuggets in the preheated oven for 20-25 minutes, flipping them halfway through. They should turn a beautiful golden brown and become crispy on the outside.
Once baked, remove the nuggets from the oven and let them rest for a few minutes on a cooling rack. This allows the exterior to set and become extra crispy.
Serve the veggie nuggets warm with your favorite dips, or enjoy them as a satisfying snack. They’re best eaten fresh but can be stored in the fridge for up to 3 days and reheated in a hot oven until crispy again.
