Heat the oven: Preheat to 425°F (220°C). Line a rimmed sheet pan for easy cleanup.
Roast the tomatoes: Toss tomatoes with olive oil, garlic, red pepper flakes, salt, and pepper.
Spread in a single layer and roast 15–20 minutes, until blistered and juicy.
Boil the pasta: While tomatoes roast, cook pasta in well-salted water until al dente. Reserve 1 cup of the starchy water before draining.
Build the sauce base: Transfer roasted tomatoes and their juices to a large skillet or the pasta pot. Add a splash of pasta water to loosen and lightly mash some tomatoes to release more juices.
Make it creamy: Off the heat, stir in ricotta, Parmesan, lemon zest, and 1–2 teaspoons lemon juice. Add a drizzle of olive oil.
Season with salt and pepper.
Toss with pasta: Add drained pasta to the sauce. Toss over low heat, adding pasta water a little at a time until glossy and silky. You want the sauce to cling, not pool.
Finish: Fold in basil.
Taste and adjust salt, pepper, and lemon. Add more Parmesan if you like.
Serve: Plate with extra cheese, a thread of olive oil, and a few basil leaves on top.