Preheat your oven to 400°F (200°C). On a baking sheet, toss the halved cherry tomatoes with olive oil, minced garlic, salt, pepper, and dried oregano. Spread them out in a single layer so they roast evenly. Roast for about 20-25 minutes, or until the tomatoes are softened, caramelized, and bursting with sweet juices.
While the tomatoes roast, bring a large pot of salted water to a boil. Add the rigatoni and cook according to package instructions until al dente—usually about 10-12 minutes. Reserve about 1/2 cup of pasta water before draining.
Transfer the drained rigatoni to a large mixing bowl. Add the roasted cherry tomatoes along with all the flavorful juices from the baking sheet. Toss gently to combine. If the mixture seems dry, splash in some reserved pasta water to loosen it up and create a silky sauce.
Place the burrata cheese on top of the pasta. You can either break it up slightly so it melts into the warm rigatoni or leave it whole for guests to cut into themselves. The burrata’s creamy center will melt beautifully, coating the pasta in a rich, luscious layer.
Scatter fresh basil leaves over the pasta and finish with a generous sprinkle of grated parmesan cheese. Serve immediately while warm and gooey for the very best experience.