Preheat the broiler. Oil a baking pan and set aside. In a large pan, saute the garlic in olive oil until browned. Remove and discard the garlic.
Add the crushed tomatoes, basil leaves, chile pepper flakes, and salt. Roughtly chop the olives and capers and add to the pan. Cook, covered, over low heat until somewhat thickened, about 10 minutes.
Meanwhile, bring a large pot of salted water to boil for cooking the pasta. When the pasta is cooked but still al dente - you need to be able to bend a strand, but it shoudn't be soft-drain the pasta in a colander.
Off the heat, add the pasta to the pan with the sauce and toss to combine. using a ladle and a large serving fork, twist about 1/4 of the pasta into a nest and place the nest in the prepared baking dish
Repeat with the remaining pasta. Place the burrata in a bowl and cut it open. Spoon the liquid from inside the burrata over the top of each nest.
Sprinkle with breadcrumbs and grated Parmesan. Broil until browned and crisp, about 5 minutes.