Finely grate the carrot and zucchini. Place grated zucchini in a clean kitchen towel or several layers of paper towel and squeeze firmly to remove as much liquid as possible. This prevents soggy balls. Finely mince the onion and garlic. Thaw peas and roughly mash with a fork.

Sweat onion and garlic (optional)

In a small skillet over medium heat add 1 tsp oil (not in ingredient list intentionally small) and sauté the minced onion and garlic just until softened and translucent, about 3–4 minutes. Let cool slightly. This mellows raw onion/garlic — you can skip this step if you prefer raw for speed.

Combine mixture

In a large bowl combine the grated carrot, squeezed zucchini, sautéed (or raw) onion and garlic, mashed peas, chopped parsley, beaten egg, 3/4 cup plain breadcrumbs, grated Parmesan (if using), salt, black pepper, dried oregano, and smoked paprika. Mix with a spatula or clean hands until evenly combined. The mixture should hold together when pressed; if too wet add up to 2 tablespoons more breadcrumbs, if too dry add a teaspoon of water or another small beaten egg.

Chill mixture

Cover the bowl and refrigerate the mixture for 20 minutes. Chilling firms the mixture so the balls hold their shape during coating and frying.

Form balls

Use a 1.5 tablespoon scoop or a small cookie scoop (or spoon) to portion mixture. Roll each portion between your palms into a compact ball about 1 to 1 1/4 inches diameter. You should get about 18–22 balls depending on size. Place formed balls on a baking sheet lined with parchment.

Coating & Frying

Set up dredging station

Arrange three shallow dishes: one with 1/2 cup all-purpose flour, one with the beaten egg, and one with 1 cup panko breadcrumbs. Lightly season the flour with a pinch of salt and pepper for better flavor.

Coat the balls

Working in batches, roll each chilled veggie ball first in the flour, shaking off excess, then dip into the beaten egg, letting excess drip off, and finally press into the panko breadcrumbs to coat fully. Place coated balls back on the parchment-lined tray. For an extra-crisp double crust, you can repeat the egg and panko step once more.

Heat oil

Pour about 1/4 to 1/2 cup oil into a large skillet (or shallow pan) so the oil is about 1/4 inch deep. Heat over medium-high until shimmering and a small piece of breadcrumb sizzles gently on contact (about 350°F / 175°C equivalent). If using a thermometer aim for 350°F; adjust heat to maintain that temperature.

Fry the balls

Carefully add coated balls to the hot oil in a single layer without overcrowding (work in batches). Fry for 2.5–3 minutes per side, turning gently with tongs or a slotted spoon, until golden brown and crisp all over. Total fry time about 5–6 minutes per batch depending on size. If the exterior browns too quickly, lower the heat slightly so the interior cooks and egg binder sets.

Drain and keep warm

Transfer fried balls to a wire rack set over a baking sheet or to a plate lined with paper towels to drain excess oil. Keep warm in a low oven (200°F/95°C) while you fry remaining batches.

Serve

Serve the crispy veggie balls hot with lemon wedges for squeezing and the dipping sauce on the side if using.

Dipping Sauce (optional)

Mix sauce

In a small bowl combine the Greek yogurt, mayonnaise, lemon juice, honey or maple syrup, smoked paprika, salt, and black pepper. Whisk until smooth. Taste and adjust seasoning — add a little more lemon for brightness or a pinch more sweetener to balance acidity.

Chill and serve

Refrigerate the sauce for 10–15 minutes to let flavors meld, then serve alongside the warm crispy veggie balls.