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Pre-heat the oven to 400°F.
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Toss the cherry tomatoes, shallots and oregano with the olive oil and balsamic vinegar in a large bowl. Stir in the basil leaves, tearing any large leaves in half. Season with salt and freshly ground black pepper.
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Place the tomatoes onto a baking sheet in one layer and transfer the sheet to the oven. Roast for 20 to 25 minutes, until the tomatoes start to burst open, stirring halfway through the cooking time.
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Bring a large pot of salted water to a boil. Cook your pasta according to package directions if using dried pasta. If you are using frozen or fresh cavatelli, add the pasta to the boiling water and boil for 5 minutes, until the cavatelli floats to the surface. Reserve 1 cup of the pasta water and then drain the cavatelli. (Do not rinse.)
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While the pasta is cooking, heat a large sauté pan over medium heat. Add the diced pancetta and cook until it is crispy. Discard some of the fat, leaving at least 1 tablespoon in the pan. Lower the heat and add the roasted tomatoes and shallots, along with any juices from the sheet pan. Add the cooked pasta, Parmesan cheese and ¼ cup of the reserved pasta water. Toss everything together in the pan, adding more pasta water if needed to loosen the sauce.
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Transfer the pasta to serving bowls. Cut open the burrata and spoon a big dollop of the cheese on each serving. Drizzle with a little olive oil and season with freshly ground black pepper. Top with a chiffonade of fresh basil leaves and serve immediately.