In a large pot, bring 4 quarts water to a boil. Add the pasta and 2 tablespoons salt, then cook, stirring occasionally, until just shy of al dente. Reserve about 2 cups of the cooking water, then drain the pasta.

In a 12-inch skillet over medium, combine the oil and tomatoes. Cook, stirring only once or twice, until the tomatoes have softened and the oil has taken on a reddish hue, 4 to 6 minutes.

Stir in half the pistachios, 1½ cups of the reserved cooking water, ½ teaspoon salt and ¼ teaspoon pepper. Bring to a simmer and cook, stirring occasionally, until the mixture is slightly reduced and the tomatoes are completely softened, about 2 minutes.

Add the pasta and lemon zest, then cook, stirring frequently, until the pasta is al dente and has absorbed most of the liquid but is still quite saucy, 2 to 4 minutes.

Off heat, stir in the mint, then taste and season with salt and pepper. If the pasta is dry, add more cooking water, 1 tablespoon at a time. Transfer to a serving bowl, then sprinkle with the remaining pistachios and drizzle with additional oil. Serve with cheese.