In a medium sized bowl, whisk the eggs and whole milk together and season with salt and pepper. Add the pasta, zucchini and cheese to the mixture and stir to combine.
Heat olive oil in a 10" oven safe skillet over medium-high heat. Pour the mixture into the pan and cook the fritatta until edges start to pull away from the pan, about five minutes.
Transfer the skillet to the oven and bake until set, about fifteen minutes.
Top with grated lemon zest, parsley, a drizzle of high quality olive oil and shaved Parmigiano Reggiano and serve.