Troffie are a type of pasta which look like very slender, elongated corkscrews, but feel free to use any thin, tube-shaped pasta such as penne. The flavor of fresh tomatoes contrasts nicely with the Ventresca tuna, a premium canned tuna packed in olive oil that comes from the belly of the fish and has a particularly rich flavor and silky texture.
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Preheat the oven to 225 degrees.
Place the cherry tomatoes on a baking sheet. Toss tomatoes in 2 ounces of the olive oil, thyme, and 1 sliced clove garlic. Roast for 1 ½ hours. Remove from the oven, let cool, and dice finely.
Bring a pot of water to a boil over high heat and prepare an ice bath. Add the heirloom tomatoes one by one and cook for 20 seconds each. Immediately plunge each tomato into the ice bath to cool. Peel the tomatoes and quarter them. Seed the tomatoes and strain the liquid into a separate bowl. Then, continue to dice the tomatoes into small pieces and place in the bowl with the juices. Discard the seeds.
Heat 2 ounces of the olive oil in a skillet over medium heat. Brown the remaining garlic for 2 minutes, then add the onion and sweat for 3-4 minutes. Add the tomato paste, diced heirloom tomatoes with juices, and diced cherry tomatoes and simmer for about 20 minutes.
Meanwhile, bring a large pot of water to a boil over high heat. Season with salt, to taste. Add the pasta and cook until just al dente, then drain and set aside.
Heat the remaining olive oil in a skillet over medium heat and fry the capers until crisp. Then, add the tomato sauce mixture, olives, lemons, and parsley. Add the pasta and toss. Plate the pasta and top with pieces of tuna and shaved cheese.