Heat the oven to 425°F. Toss tomatoes, garlic, olive oil, red pepper flakes, salt, and black pepper on a sheet pan. Roast until the tomatoes burst and the edges begin to caramelize.

Cook pasta in well-salted water until just al dente. Reserve a cup of pasta water, then drain.

Add pasta to the pan of roasted tomatoes. Toss well, adding splashes of pasta water until the tomato juices coat the noodles.

Transfer to a serving platter. Tear burrata over the warm pasta, then add basil, Parmesan, and a light drizzle of balsamic vinegar if using.

Serve right away, allowing everyone to mix the creamy burrata through their portion.