Ingredients

• 7 garlic cloves, finely grated
• 1 1/2 lb. cherry tomatoes (about 2 pints), halved
• 1 1/2 cups (lightly packed) coarsely chopped basil, plus leaves for serving
• 1/2 cup extra-virgin olive oil
• 2 Tablespoons Calabrian chile paste
• 2 teaspoons Diamond Crystal or 1 1/4 teaspoon Morton kosher salt, plus more
• 3/4 teaspoons freshly ground pepper, plus more
• 12 oz. dried lumache (snail shells) or other medium shell pasta
• 3 oz. Parmesan, finely grated (about 1 1/2 cups), plus more for serving
• 5 Tablespoons unsalted butter, cut into 1/2 inch pieces

Procedure

1. Combine garlic, cherry tomatoes, basil, olive oil, Calabrian chile paste, salt, and  freshly ground pepper in a large bowl.
2. Using your hands or a potato masher, crush tomatoes to release their juices and break up into small pieces.
3. Let cherry tomato mixture sit at room temperature at least 10 minutes and up to 1 hour.
4. Meanwhile, cook pasta in a large pot of boiling heavily salted water, stirring occasionally, until al dente. Drain, reserving 1 cup pasta cooking liquid. Shake pasta to remove excess water; return to pot.
5. Immediately add Parmesan and butter, to pasta and vigorously stir until butter and cheese are melted. (If pasta seems dry, add some cherry tomato mixture a spoonful at a time as needed and keep stirring until cheese is melted and emulsified.)
6. Add cherry tomato mixture and toss, adding reserved pasta cooking liquid a splash or so at a time as needed, until sauce is creamy and coats pasta. Taste pasta and season with more salt and pepper if needed.
7. Divide pasta among shallow bowls and top with more Parmesan and some basil leaves.