Bring a large pot of salted water to a boil. Cook the pasta according to the package directions. Reserve 1 cup of the pasta cooking water and drain the rest.
Whisk together the eggs, lemon zest and juice, and pesto.
In a large skillet, heat the oil over medium-high heat. Add the onion and cook until translucent, about 5 minutes. Add the garlic and cook, stirring, for 30 seconds. Add the pasta, turkey, ½ cup pasta water, and pesto sauce. Stir to combine and take off the heat – do not leave on heat too long or it will curdle. If the sauce seems too thick, add a little more of the pasta water. Stir in the Parmesan cheese and parsley and serve.