Start by grating the carrots and zucchini finely using a food processor or a box grater. Place the grated vegetables in a clean kitchen towel or cheesecloth and squeeze out as much excess moisture as possible—this helps the nuggets stay crispy.
Pour the grated and drained vegetables into a large mixing bowl. Add in the beaten eggs, panko breadcrumbs, garlic powder, paprika, salt, and pepper. Mix everything thoroughly until well combined; the mixture should hold together when pressed.
Shape the mixture into small, compact nuggets about 2 inches long and 1 inch wide. Keep your hands slightly damp to prevent sticking and help form neat shapes.
Heat oil in a frying pan over medium heat until it shimmers, or preheat your oven to 200°C (390°F) and line a baking sheet with parchment paper. If baking, brush the nuggets lightly with oil for extra crispiness.
Place the nuggets carefully into the hot oil, cooking in batches if needed. Fry for about 3-4 minutes per side, until they are golden brown and crispy, or bake for 20-25 minutes, flipping halfway through, until evenly golden and crispy.
Once cooked, transfer the nuggets to a paper towel-lined plate if fried to drain excess oil, or leave on the baking sheet for a few minutes if baked to crisp up further.
Serve the veggie nuggets hot, accompanied by your favorite dips or ketchup, and enjoy their crispy exterior with a tender, veggie-packed interior.
