Begin by heating the olive oil in a large skillet over medium heat. Add the onion and carrots, sautéing until they soften, about 3-4 minutes. Next, toss in the zucchini and mushrooms, cooking until they’re tender and the moisture has evaporated. Finally, stir in the spinach and cook until wilted. Season with salt and pepper to taste. Remove from heat and set aside.
In a large mixing bowl, combine the crushed tomatoes, tomato sauce, and tomato paste. Stir in the Italian seasoning, sugar, and chopped basil. Taste and adjust seasoning with salt and pepper as desired.
In a large pot, bring salted water to a boil. Cook the lasagna noodles according to package instructions until al dente. Drain and lay them flat on a clean surface to prevent sticking.
In a separate bowl, combine the ricotta cheese, grated parmesan, and egg. Mix until well combined, then season with a pinch of salt and pepper.
Preheat your oven to 375°F (190°C). In the bottom of a 9x13 inch baking dish, spread a thin layer of the tomato sauce. Layer 3 lasagna noodles over the sauce, followed by half of the vegetable mixture, then half of the ricotta mixture, and a third of the mozzarella cheese. Repeat the layers, finishing with a final layer of noodles topped with the remaining sauce and the rest of the mozzarella cheese.
Cover the baking dish with aluminum foil (to prevent sticking, spray the foil with cooking spray) and bake for 25 minutes. Remove the foil and bake for an additional 25 minutes, until the cheese is bubbly and golden. Let the lasagna sit for 10-15 minutes before slicing to allow it to set.