Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper.

In a bowl, toss the halved cherry tomatoes with 2 tablespoons of olive oil, salt, and black pepper. Spread them out on the prepared baking sheet in a single layer.

Roast the tomatoes in the preheated oven for 20-25 minutes, or until they are soft and slightly caramelized.

While the tomatoes are roasting, cook the pasta according to package instructions in a large pot of salted boiling water. Reserve 1/2 cup of pasta water, then drain the pasta.

In a large mixing bowl, combine the cooked pasta, roasted tomatoes, and pesto. If the mixture seems dry, add a little reserved pasta water until you reach your desired consistency.

Tear the burrata cheese into pieces and gently fold it into the pasta mixture. Be careful not to break it up too much.

Serve the pasta in bowls, topped with grated Parmesan cheese and fresh basil leaves.