Cut the cherry tomatoes in half. Smash the garlic cloves with the side of a large knife and remove skins. 

Heat the olive oil in a large pan (large enough to hold all the pasta) over medium low heat.  Add the garlic cloves and red pepper flakes. Cook for 30 seconds. Add in the cherry tomatoes, a few large pinches of salt and a few grinds of black pepper. Continue cooking over medium heat, stirring occasionally, until the tomatoes begin to break down, about 10 minutes.  Taste and adjust salt and pepper if needed. 

Meanwhile, bring a large pot of water to a boil. Season generously with salt. Cook the pasta, according to package directions, until al dente. (If sauce finishes before pasta is ready, simply turn off the heat and allow the sauce to rest until your pasta is cooked.  Turn heat back on just before pasta is ready.) 

When the pasta is almost ready, remove the garlic cloves from the sauce. Tear the basil leaves and add to the sauce. Generously grate Parmigiano over the sauce. Stir to incorporate. 

Reserve 1/2 cup of the pasta water. Drain the pasta and toss it into the pan with the sauce.  Stir to coat the pasta with the sauce. If dry, add a little of the pasta water and stir again. Allow the pasta to simmer for a minute in the sauce. 

Plate the pasta on a large serving platter. Tear the burrata over the warm pasta and sprinkle with more grated Parmigiano.  Serve!