Peel onions and cook in boiling salted water for about 5 minutes. Pour into a sieve and drain. Hollow out the inside of the onion with a small knife.
Drain the tuna in a sieve. Put it in a bowl and tear it up with a fork. Drain capers and chop. Wash parsley, shake dry. Pluck leaves and chop finely. Drain tomatoes and cut into small pieces. Mix tuna with capers, tomatoes and parsley. Season to taste with salt and pepper.
Grate the Parmesan finely and mix with breadcrumbs. Add the tuna mixture to the hollowed onions. Place the onions next to each other in 2 ovenproof casseroles (each approx. 15 cm Ø; or in a large dish of approx. 23 cm Ø). Sprinkle with the Parmesan mixture and drizzle with olive oil. Bake in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) for 10-15 minutes. Remove and serve.