Bring a large pot of generously salted water to a boil.
Cook the pasta until al dente according to package directions.
Reserve approximately 1 cup of pasta water before draining.
Meanwhile, heat the olive oil in a large skillet over medium heat.
Add the cherry tomatoes and season lightly with salt and black pepper.
Cook for 6–8 minutes, stirring occasionally, until the tomatoes begin to blister and soften.
Add the garlic and red pepper flakes and cook for 30–60 seconds.
Continue cooking for another 4–6 minutes until several tomatoes burst.
Gently press some of the softened tomatoes with the back of a wooden spoon, leaving others partially intact.
Add the drained pasta to the skillet with approximately 1/4 cup reserved pasta water.
Toss until the tomato juices and olive oil form a light sauce that coats the pasta.
Add additional pasta water as needed.
Remove from the heat and toss with most of the fresh basil.
Transfer the pasta to a serving bowl or individual plates.
Place the burrata over the warm pasta and gently tear it open.
Finish with remaining basil, black pepper, a drizzle of olive oil, Parmesan, and red pepper flakes if desired.
Serve immediately.