Preheat oven to 350°F (175°C).
In an 8-inch cast iron skillet, combine the cherry tomatoes and whole peeled garlic cloves.
Sprinkle in the chopped rosemary, thyme, red pepper flakes, salt, and black pepper. Drizzle olive oil over everything. Toss directly in the pan until everything is evenly coated.
Place the skillet in the center of the oven and roast for 25 minutes, until the tomatoes are soft, blistered, and just starting to burst, and the garlic is tender. Start checking at the 20-minute mark.
Remove the skillet from the oven and turn the oven off. Using a fork, lightly mash all of the roasted garlic cloves and about half of the tomatoes. Stir gently to incorporate the garlic paste and tomato juices into the oil and spices, creating a rustic sauce.
Create four small wells in the tomato mixture. Gently place one mini burrata ball into each spot. Using a spoon, drizzle a bit of the warm tomato oil mixture over the tops of the burrata.
Return the skillet to the still-warm (but off) oven for about 1 minute, just long enough for the burrata to warm through and become creamy in the center without melting completely.
Finish by sprinkling freshly grated Parmesan over the top and garnish with fresh basil leaves. Serve immediately straight from the skillet with toasted flatbread, pita, or baguette slices for scooping.