Begin by preheating your oven to 375° F.
Heat olive oil in a large skillet or Dutch oven pot over medium-high heat. Add onion, bell pepper, mushrooms, and zucchini, and cook until they are softened, stirring occasionally. Add minced garlic and cook for another 30 seconds.
Add marinara sauce, Italian seasoning, salt, pepper, red pepper flakes, and parsley to the skillet and stir. Bring to a simmer and then reduce the temperature to low. Cook at a low simmer for 10 to 15 minutes, stirring occasionally. Add chopped fresh spinach and stir.
In a medium bowl, crack the egg and beat it lightly with a fork. Add ricotta cheese and stir to combine. Also, shredded mozzarella cheese at this time.
To assemble the lasagna, take a 9x13-inch baking dish and put about 1 cup of the sauce into it. Lay three lasagna noodles evenly over the sauce. Spread ⅓ of the remaining sauce over the noodles. Put small spoonfuls of the ricotta and egg mixture on top of the sauce, using half of the ricotta. Sprinkle ⅓ of the mozzarella and ⅓ of the Parmesan over the top.
Repeat the previous layer: three noodles, ½ of the remaining sauce, the rest of the ricotta, ½ of the remaining mozzarella, and ½ of the remaining Parmesan. For the top layer of the lasagna, use the remaining 3 noodles, the rest of the sauce, and finally, the rest of the mozzarella and Parmesan.
Cover the lasagna with a piece of foil that has been sprayed with cooking spray on the underside to prevent the cheese from sticking to the foil.
Bake the lasagna in the center of the oven, covered with foil, for 35 minutes. Place a rimmed baking sheet on the rack below the lasagna to catch any drips of sauce. Then uncover and continue baking for 10 to 15 minutes more, or until the lasagna is hot and bubbling on the sides and the cheese is lightly browned on top. Let the lasagna rest for 15 minutes before serving, and do not skip this step, or the lasagna will be too soupy when serving.