Tip: Store nuts in the fridge or freezer to keep their oils from spoliling.
Bring a large pot of water to a boil for the pasta.
If the nuts aren’t roasted, in a small skillet, cook the nuts over medium heat, stirring occasionally, until fragrant, about 3 minutes. Let cool. Finely chop the nuts. (Or place the nuts in a food processor and pulse a few times until finely chopped.)
In a large deep skillet with a lid, heat the olive oil, about four turns of the pan, over medium. Add the tomatoes. Cover and cook, shaking the skillet often, until the tomatoes slump, 10 to 15 minutes; season with salt and pepper.
On a work surface, chop or grate the garlic. To make the gremolata, pile the mint, parsley, and lemon zest on top of the garlic. Finely chop everything together until evenly incorporated.
Salt the boiling water and add the pasta. Cook until 1 minute shy of the package directions. Reserve 1/2 cup of the cooking water and drain the pasta.
Stir half the nuts, all the gremolata, and the chile paste into the tomatoes; season with salt. Add the pasta and about 1 cup cheese; toss, until evenly incorporated, about 1 minute. Add the cooking water if the pasta seems dry.
Serve in shallow bowls and top with the remaining nuts. Serve with EVOO for drizzling and more cheese for sprinkling.