For the white sauce: Bring a medium saucepan to low-medium heat and add the butter. Once the butter is melted, stir in the flour with a wooden spoon; cook for 2 minutes (do not let it color). Add the milk and bring to a boil, continuing to stir. Reduce the heat to medium-low and simmer for 1 minute. Remove the saucepan from the heat. Add in the Parmesan, whisking to incorporate. Season with salt and pepper.
For the lasagna: In a skillet over medium-high heat, add the olive oil and cook the turkey sausage until just beginning to brown, about 4 minutes. Add the mushrooms and continue to saute until golden brown and the turkey is cooked through, 4 to 6 additional minutes. Season with kosher salt, pepper and granulated garlic. Stir well, and then shut off the heat and set aside to cool.
In a small mixing bowl, combine ricotta, egg, Parmesan, about 1/2 teaspoon coarse salt and a few rounds of cracked pepper. Spread 1/4 cup of the white sauce in the bottom of a 9- by 13-inch nonreactive baking dish. Begin layering with 3 noodles, followed with about 1 cup ricotta mixture. Layer about half of the zucchini evenly over the ricotta. Follow with half the turkey sausage and mushrooms, finishing with 1 cup white sauce. Sprinkle with 1/3 of the mozzarella. Repeat. Top the second layer with 4 noodles, white sauce and sprinkle with the remaining mozzarella. Bake, covered with foil, for 30 minutes.
Remove from the oven and remove the foil cover. Heat the broiler to maximum temperature. Broil until the cheese is browned and bubbling, about 1 minute. Garnish with the parsley.
To help eliminate a mess in the oven, add the baking dish to a parchment-lined baking sheet to catch anything that bubbles over.