Ingredients

1 1/2 pounds ripe medium tomatoes, cored and torn, or chopped into 1/2-inch pieces (3 cups)

1/2 cup plus 2 tablespoons extra-virgin olive oil

2 cloves garlic, smashed and peeled

1/4 cup packed fresh basil leaves, torn, plus more for serving

1 teaspoon red-wine vinegar

1/4 teaspoon red pepper flakes

Kosher salt

12 ounces spaghetti

2 jars (each 7 ounces) tuna packed in oil, drained

1 ounce Parmigiano-Reggiano, grated (1/4 cup), plus more for serving

Preparation

In a large heatproof bowl, combine tomatoes, 1/2 cup oil, garlic, basil, vinegar, and red-pepper flakes. Season generously with salt. Let stand up to 1 hour; remove and discard garlic.

Cook pasta in a large pot of generously salted water according to package directions until al dente. Reserve 1/4 cup pasta water, then drain.

Immediately transfer pasta to bowl with tomatoes; add tuna, cheese, and remaining 2 tablespoons oil. Toss well to combine, adding pasta water as needed to create a silky sauce. Serve with more cheese and basil.