Preheat your oven to 400°F (200°C). In a mixing bowl, combine the cherry tomatoes, minced garlic, thyme, olive oil, kosher salt, and black pepper. Toss everything together until the tomatoes are well-coated. Spread them out on a baking sheet and roast for about 30-40 minutes, or until they burst and become soft, filling your kitchen with a delightful aroma.

While the tomatoes are roasting, take your fresh burrata and gently remove it from its packaging. Using a sharp knife or syringe, carefully create an opening in the burrata's outer shell. Spoon or inject your choice of pesto into the creamy center, ensuring that it fills without tearing the cheese. Set aside to allow the flavors to meld.

Once the tomatoes are perfectly roasted, remove them from the oven and let cool slightly. On a serving platter, place the beautiful pesto-stuffed burrata in the center. Arrange the warm roasted cherry tomatoes around the burrata, showcasing their vibrant colors. This presentation will make the Pesto-Stuffed Burrata Bombs truly eye-catching.

Drizzle some extra-virgin olive oil over the burrata and tomatoes for added richness. Finish the dish with a sprinkle of flaky sea salt and some fresh basil leaves for brightness and flavor. Serve immediately while the cheese is warm and creamy, inviting your guests to dip and indulge in the delightful flavors of your Pesto-Stuffed Burrata Bombs.