Peel and chop the carrots and zucchini into small pieces. Steam or boil until very soft, about 8-10 minutes, until they easily mash and are tender.
Drain the cooked vegetables thoroughly and mash them together in a large bowl until smooth, leaving some tiny bits for texture. Let them cool slightly so the mixture isn’t too hot to handle.
Add the shredded cheese, salt, pepper, and paprika to the mashed vegetables. Mix well to distribute the seasonings evenly and melt the cheese into the mash.
Pour in the beaten egg (or flaxseed mixture) and stir until the mixture is sticky and holds together. If it feels too loose, sprinkle in a few more breadcrumbs and mix again.
Scoop about a tablespoon of the mixture, then gently roll and shape it into a small nugget, pressing slightly to flatten. Repeat with the remaining mixture, placing the formed nuggets on a plate or tray.
Heat oil in a frying pan over medium heat until shimmering and hot (about 160°C/320°F). Carefully place the nuggets into the pan, making sure not to overcrowd, and cook for about 3-4 minutes per side until they turn golden brown and crispy.
Alternatively, preheat your oven to 200°C/400°F and line a baking sheet with parchment paper. Arrange the nuggets on the sheet, brush lightly with oil, and bake for 15-20 minutes, flipping halfway, until they are crispy and golden.
Once cooked, transfer the nuggets to a paper towel-lined plate to drain excess oil if fried. Let them rest for a minute or two, then serve hot with your favorite dipping sauce.
