1. Preheat the oven to 425°F. In a baking dish, toss the tomatoes with the olive oil, 2 tablespoons of herbs, garlic, salt, and pepper. Arrange the prosciutto around the tomatoes. Roast for 10–15 minutes, until the tomatoes burst and the prosciutto is crisp.2. Meanwhile, whisk the egg yolks, whole egg, and Parmesan together in a large serving bowl. Add the butter.3. Cook the pasta until al dente. Just before draining, reserve 1 cup of the pasta cooking water, then drain.4. Immediately add the hot pasta to the egg mixture, tossing quickly to combine. Add the hot pasta water a little at a time, tossing continuously, until the sauce is creamy and glossy. Add the roasted tomatoes and all their juices. Crumble in the crispy prosciutto and gently toss. Season with freshly cracked black pepper.5. Divide the pasta among plates. Top with torn burrata, basil, and Calabrian chilies. Serve immediately and start twirling!