Preheat the oven to 400 degrees F. Toss the tomatoes with 2 tablespoons olive oil, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. Spread the tomatoes on a rimmed baking sheet and roast until softened, about 20 minutes. Return to the bowl and stir with a wooden spoon to break up the tomatoes and make a chunky sauce.
Meanwhile, bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1/2 cup cooking water, then drain.
While the pasta is cooking, heat the remaining 2 tablespoons olive oil in a small skillet over medium heat. Add the garlic and cook, stirring occasionally, until lightly golden, about 3 minutes; add to the bowl with the tomatoes.
Add the pasta to the tomato mixture and toss, adding enough of the reserved pasta cooking water to loosen the sauce. Stir in the oregano and season with salt and pepper. Top each serving with the burrata, basil, a drizzle of olive oil and a few grinds of pepper.
Cook's Note: Burrata is fresh mozzarella that's filled with cream and curds, so it oozes when cut. If you can't find it, top your pasta with ricotta instead.
Burrata is fresh mozzarella that's filled with cream and curds, so it oozes when cut. If you can't find it, top your pasta with ricotta instead.