Rinse tuna, dab dry and cut into 2.5 cm thick steaks. Season well with salt and pepper. Place in an ovenproof dish and sprinkle with lemon juice, then pour olive oil over it.
Scratch tomatoes crosswise. Scald with boiling hot water. Quench cold and peel the skin. Wash the herbs, shake dry, pluck smaller and place between the tuna steaks.
Cover and leave to marinate cold for about 1 hour.
Preheat oven (electric cooker: 175 °C/circulating air: 150 °C/gas: see manufacturer). Turn the tuna and cook in the oven for approx. 8 minutes. Remove from the oven. Turn the tuna over again and cook in the hot tuna stock for approx. 30 minutes.
Peel the shavings from the Parmesan cheese with a peeler and sprinkle over the tuna. You can serve it with focaccia or ciabatta.