In a large pot of salted boiling water, cook the pasta according to the package instructions until al dente. Reserve about 1 cup of pasta water, then drain the rest and set the pasta aside.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 30 seconds until fragrant, being careful not to burn it.
Add the halved cherry tomatoes to the skillet and season with salt, pepper, and red pepper flakes. Cook, stirring occasionally, for about 5-7 minutes until the tomatoes soften and start to burst, releasing their juices.
Add the cooked pasta to the skillet with the tomatoes. Toss everything together, adding reserved pasta water a little at a time to create a light sauce that coats the pasta. Cook for an additional 1-2 minutes until heated through.
Remove the pan from heat. Transfer the pasta to serving plates or a large serving bowl. Tear the burrata into pieces and place it on top of the pasta.
Sprinkle lemon zest over the dish and garnish with fresh basil leaves. Drizzle with a bit more olive oil if desired, and serve immediately.