Preheat the oven to 375°F (190°C).
Heat the cast-iron or oven-proof skillet over medium heat and add the olive oil.
Add the diced onion and cook, stirring frequently, until it begins to soften, about 3–4 minutes.
Add the diced garlic and sauté for about 1 minute until fragrant.
Add the diced zucchini and sliced mushrooms and cook for 3–4 minutes until the zucchini is tender and mushrooms have softened.
Pour in the Italian tomato sauce and stir to combine; warm the sauce over medium heat for a minute or two.
Stir in the baby spinach and cook 1 minute until wilted, then season the sauce with salt and pepper to taste. Remove the pan from the heat.
Spoon out and set aside all but 1 cup of the sauce from the pan. Spread the remaining sauce evenly over the bottom of the skillet.
Cover the sauce with a single layer of broken lasagna noodle pieces, overlapping as needed to mostly cover the sauce.
Dollop about one-third of the ricotta in 5–6 mounds over the noodles, then spread one-third of the reserved sauce over the ricotta and sprinkle with one-third of the mozzarella.
Add another layer of noodles and repeat: ricotta (one-third), sauce (one-third), and mozzarella (one-third).
Top with a final layer of noodles, spoon the remaining sauce over them, add the remaining ricotta, sprinkle the remaining mozzarella, and finish with the shredded Parmesan.
Transfer the skillet to the preheated oven and bake about 30 minutes, until the cheese is bubbly and the pasta is cooked through.
Remove from the oven and let cool for about 5 minutes before serving.
