Cook the Pasta: Bring a large pot of salted water to a boil. Add the penne pasta and cook according to package instructions until al dente. Reserve 1 cup of pasta water before draining.
Sauté Vegetables: While the pasta cooks, heat olive oil in a large skillet over medium heat. Add the garlic and shallots, and sauté until fragrant and translucent. Add the chopped eggplant and green beans. Pour in about half of the reserved pasta water, cover, and let the vegetables steam for about 5-7 minutes, or until they begin to soften.
Simmer with Tomato Puree: Uncover and stir in the tomato puree, dried oregano, sea salt, crushed red pepper, and black pepper. Let the sauce simmer for another 5 minutes, allowing the flavors to meld.
Combine Pasta and Sauce: Add the cooked, drained pasta to the skillet with the vegetable and tomato mixture. Toss well to coat the pasta evenly. If the sauce is too thick, add more reserved pasta water to reach desired consistency.
Serve with Burrata: Transfer the pasta to serving bowls. Top each serving with torn burrata cheese and, if using, sprinkle with fresh herbs for an added burst of flavor.
