Preheat oven to 375°F.
In a small baking dish, combine cherry tomatoes, olives, smashed garlic, 1 tablespoon oregano, olive oil, lemon peel, salt, and red pepper flakes.
Roast for about 40 minutes, until the tomatoes are soft, jammy, and release their juices, and the garlic is tender.
Remove from the oven and let cool slightly for 5–10 minutes.
Place the burrata on top and gently tear it open to spread slightly. Spoon some of the warm cooking juices over the cheese.
Finish with the remaining oregano and serve immediately with toasted bread or fresh baguette.