Preheat oven to 300 degrees. Place the tomatoes in a single layer in a baking dish. Add the garlic slices and basil sprigs. Pour the oil over the tomatoes and season generously with salt and pepper. Add a touch of chili flakes to taste. Bake for 1 hr.
While the tomatoes are in the oven fill a large pot with salted water and cook the pasta, according to the package instructions, until al dente, drain and put in a serving bowl.
Remove the tomatoes from the oven, discard the basil sprigs and pour the olive oil from the tomatoes on top of the pasta and toss gently.
Place the cherry tomatoes and garlic on top of the pasta and toss lightly, preferably with your hands.
Break chunks of burrata off and place on top of the pasta.
Season, to taste, with more salt, pepper, and chili flakes.