Peel and finely mince the half onion and the celery stalk. Heat 1.5 tbsp olive oil in a small skillet over medium heat. Sauté the onion and celery until soft and translucent, about 5–7 minutes. Remove from heat and let cool to room temperature.

Make polpette mixture

Place the ground beef in a large mixing bowl. Add the mashed potato, cooled sautéed aromatics, eggs, grated cheese, chopped parsley, lemon zest (finely grated), salt and pepper.

Mix gently with your hands or a spoon until just combined — avoid overworking to keep meatballs tender. Taste a small raw pinch (optional) by quickly frying a little bit of mixture to check seasoning and adjust salt/pepper as needed.

Shape the mixture into meatballs about 1.5–2 inches (3.5–5 cm) in diameter. You should get roughly 12–14 polpette depending on size.

Place the flour in a shallow dish and lightly dredge each meatball to coat. Shake off excess flour and set on a tray.

Cook polpette

Heat 4 tbsp olive oil in a large nonstick skillet over medium heat. When hot but not smoking, add the meatballs in a single layer without crowding (work in batches if necessary).

Cook the polpette, turning occasionally, until golden brown on all sides, about 8–10 minutes total depending on size. The exterior should be nicely browned.

If you prefer them finished in broth (bollito style), transfer browned polpette to a saucepan and add the 500 ml boiling broth or water. Bring to a gentle simmer, cover, and poach for 8–10 minutes until cooked through (internal temperature 70–72°C / 160–165°F). If you prefer purely pan-fried, continue cooking in skillet over lower heat, covered, for 6–8 more minutes to ensure doneness.

Finish and serve

Remove polpette from pan or saucepan and drain briefly on paper towels. If you used broth, spoon a little of the cooking liquid over the polpette for extra moisture.

Arrange polpette on a serving plate, garnish with additional chopped parsley and a light grating of cheese if desired. Serve with lemon wedges for squeezing over the meatballs.