II like yellowfin or albacore tuna the best, and I use the belly cut because it's the fattest. 

No matter how I plan to serve the tuna, I first cut it in chunks and season it with sea salt and pepper. If you just season your oil, it doesn't penetrate the fish. I cover the tuna with oil in a pot, add two cloves of garlic, bring up the heat and then let it barely simmer for 10 minutes. I add bay leaves and lemon thyme. Regular thyme and lemon zest are a good substitute. Then I let it sit for at least an hour.
 
I often put the cooked tuna in oil and seal it in canning jars, but you can refrigerate it for a few days. Just bring it to room temperature before you use it. You can even serve it warm, chunks of it over spaghetti with black olives and some of the oil. Or with a white bean salad. Or over ripe tomatoes. But it's no good piping hot or ice cold.

I like to mix it in a salad with romano beans, the flat green beans that are so meaty, like filet mignon. They're better than regular green beans but you can use them if you can't find the romanos. I cook the beans in lots of salted water until they're tender. I don't like those crunchy little French beans. I've noticed that even in France they're now cooking vegetables until they're tender. And in Italy the vegetables are always well-cooked. 

I also put salted anchovies in the salad. I soak them first to get rid of some of the salt, but you need something salty. Like the anchovies. Or some nice Calabrese olives with their anise flavor. Or big capers. I toss everything with a dressing made from Italian red wine vinegar, some extra virgin olive oil and some of the oil from the tuna. The dressing has to be fairly acidic: two to one, oil to vinegar, instead of three to one. 

I like to keep the tuna chunky, not break it up too much. It's a rustic dish, and you want to serve it looking rustic. Toss it like a salad on a big platter. A glass of wine, some crusty bread and the salad are all you need for lunch on a hot day.