1. Cook the spaghetti according to package instructions in salted boiling water until al dente. Reserve 1 cup of pasta water and drain the rest.
2. In a skillet over medium heat, add the prosciutto slices and cook until crispy, about 4-5 minutes. Remove from the skillet and set aside on paper towels.
3. In the same skillet, add minced garlic and sauté until fragrant, about 1 minute. Add the spiralized zucchini and cook for 2-3 minutes until just tender.
4. In a bowl, whisk together the eggs and Parmesan cheese until well combined.
5. Add the drained spaghetti to the skillet with zucchini, remove from heat, and quickly pour the egg mixture over the pasta, tossing vigorously to create a creamy sauce (add reserved pasta water as needed to achieve desired consistency).
6. Season with salt and pepper to taste.
7. To serve, plate the carbonara topped with crispy prosciutto, burrata cheese, and fresh basil leaves.