Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper and arrange the prosciutto in an even layer. Transfer to the oven and cook 8-10 minutes, until the prosciutto is crisp.Meanwhile, whisk together the eggs, parmesan, garlic, basil, thyme, and chives, in a large serving bowl.Bring a large pot of salted water to a boil. Boil the orzo until al dente. Before draining, scoop out about 1 cup pasta water, then drain.Immediately add the hot orzo 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. Add the butter and spinach and gently toss to combine. Season with salt and pepper. Divide the orzo among plates and top with freshly torn burrata cheese, the crispy prosciutto, and fresh herbs. Drizzle a bit of olive oil over top. Enjoy!