Cut the chicken breasts in half lengthwise and place 4 cutlets on a cutting board, sprinkle with grated parmesan and lemon zest on one side, then wrap each chicken breast with 1 or 2 slices of prosciutto. How many slices you need will depend on the size of chicken breasts and the width of the prosciutto slices. Set aside till needed.
Get the pasta cooking in large pot of salted water according to package instructions
Heat 1 tbsp of olive oil in a frying pan and pan fry the wrapped chicken breasts for 5 minutes on one side, then flip over and cook for 3-4 minutes longer until fully cooked and the prosciutto is crispy. If unsure, check the internal temperature of the thickest part of the chicken, it should read 74C/165F. Let the chicken rest until the pasta is ready.
Lower the heat to low and wipe the pan clean with a paper towel. Add the butter and let it melt add the double/heavy cream and let it heat for about 5 minutes, then sir the grated Parmesan and allow the cheese to melt slowly into the sauce, continue stirring until the sauce comes together, then sprinkle with the nutmeg and take it off the heat.
Drain the pasta and reserve 125ml/½ cup of the pasta water, add the pasta to the pan with the sauce and toss gently to coat, season with salt to taste, add a splash of the reserved pasta water to loosen the sauce if it gets too thick. Top with the sliced chicken and serve.