Bring a large pot of salted water to a boil. Cook pasta until just shy of al dente (about 1–2 minutes less than package directions). Reserve 1 cup pasta water, then drain.

Heat 3 tablespoons olive oil in a wide skillet over medium-high heat. Add cherry tomatoes in a single layer and let blister undisturbed 2–3 minutes. Shake or stir and cook another 2 minutes until many have burst and released juices.

Reduce heat to medium. Push tomatoes to the side and add reserved tablespoon olive oil and sliced garlic. Cook 30–45 seconds until fragrant and lightly golden, then combine with tomatoes. Add red pepper flakes if using.

Add drained pasta to the skillet with 1/3 cup reserved pasta water. Toss vigorously to emulsify the sauce. Stir in Parmesan and butter, and add lemon juice and zest if desired. Add more pasta water to reach desired sauciness.

Tear fresh basil over the pasta, toss once, and serve immediately with extra Parmesan.