Preheat the oven to 375 F and lightly grease an 8×8″ casserole dish. Add about 1/2 cup of dairy-free alfredo to the base of the casserole dish. Set aside.
Fill a large pot with water and bring it to a boil. Add the lasagna sheets about 2-3 at a time and cook for 3-4 minutes, until lightly tender. Transfer to a clean plate and coat lightly with olive oil to prevent sticking. Set aside.
Prepare the filling by combining the ricotta, egg, salt, pepper, garlic and onion powder in a bowl. Combine the chicken with 1/2 cup of alfredo, the shredded zucchini, and about half of the chopped prosciutto in a separate bowl.
Prepare the lasagna roll-ups by laying out a lasagna sheet and adding a few spoonfuls of the ricotta mixture and spread to evenly distribute. Add a large spoonful of the chicken mixture and spread. Roll into a tight roll. Transfer to the baking dish and repeat with all of the lasagna sheets.
Top the lasagna rolls with the remainder of the alfredo sauce and evenly spread. Add a bit of buffalo mozzarella to the top of each roll-up.
Cover and bake in the oven for 30 minutes. Remove the cover and top with the remainder of the prosciutto. Bake for another 10 minutes or until the lasagna is tender and the prosciutto is lightly crisp.
Serve topped with chopped parsley.