Preheat oven to 425°F (220°C).

Toss cherry tomatoes and garlic with 2 tbsp olive oil, salt, pepper, and red pepper flakes on a rimmed baking sheet. Roast for 25–30 minutes until tomatoes are blistered and garlic is soft.

While tomatoes roast, bring a large pot of salted water to a boil and cook spaghetti 1–2 minutes shy of al dente (9–11 minutes depending on pasta). Drain and reserve 1 cup of pasta water.

In a skillet, heat 1 tbsp olive oil over medium heat. Sauté the smashed roasted garlic for 30 seconds, add roasted tomatoes and juices, then pour in the tomato sauce and balsamic vinegar. Simmer for 8–10 minutes to meld flavors.

Toss drained pasta with the sauce and torn basil, adding 1/4 cup reserved pasta water if dry. Mix until glossy and well coated.

Transfer half the pasta to an oven-safe baking dish, sprinkle half the mozzarella and Parmesan, add remaining pasta, and finish with the rest of the cheeses. Bake for 15–20 minutes until bubbling; broil for 2–3 minutes for a golden top.