Preheat the oven to 400° F. Line a baking sheet with parchment paper and arrange the prosciutto in an even layer. Add the garlic and toss with olive oil. Bake 8-10 minutes, until the prosciutto is crisp and the garlic roasted. Meanwhile, place the zucchini in a colander. Toss with a tiny pinch of salt.whisk together the eggs, parmesan, pecorino, garlic, basil, thyme, chili flakes, lemon zest, salt, and pepper in a large serving bowl.Bring a large pot of salted water to a boil. Boil the pasta until al dente. Before draining, scoop out about 1 cup of the pasta water, then drain directly over the zucchini. This will heat the zucchini. Immediately add the hot pasta to the egg/cheese mixture, tossing quickly (to ensure the eggs do not scramble) until the eggs thicken and create a sauce. Thin the sauce with a bit of the reserved pasta water, until it reaches your desired consistency. Be careful when adding the water, the zucchini will naturally release some water into the sauce. Season with salt and pepper.Serve topped with freshly torn burrata, prosciutto, and herbs. Enjoy!