Using a sharp knife, very thinly slice the zucchini and carrot (for large zucchini, first cut in half or in quarters). Set aside.
Add the olive oil to a large pan over medium-high heat. Once warm, add the ground beef, using a wooden spoon to break it apart into small pieces. Cook for about 5–10 minutes, until almost cooked through.
Add the sliced zucchini and carrots and stir to combine. Add the tomato sauce, water, salt, and pepper and stir.
Using your hands, break the lasagna noodles into small 1-inch pieces. Add to the skillet and stir.
Cover and bring to a boil. Then reduce the heat to medium and let gently boil for about 10 minutes, until the lasagna noodles are soft, stirring occasionally so they stay submerged and don’t stick to the bottom.
Using a spoon, add dollops of ricotta cheese on top of the skillet. Sprinkle evenly with parmesan and then mozzarella.
Place in the oven to broil for about 5 minutes, until the cheese is melted and golden.