Step 1: Heat olive oil in a large (12-inch or larger) high-sided skillet or Dutch oven over medium-high heat. Add ground beef (or sausage) and cook, breaking it apart with a spoon, until browned and cooked through, about 5-7 minutes. Drain any excess grease.
Step 2: Add diced onion to the skillet and cook until softened, about 5 minutes. Stir in minced garlic and Italian seasoning, and cook for another minute until fragrant.
Step 3: Pour in crushed tomatoes, tomato sauce, water or broth, salt, and pepper. Stir well to combine. Bring the sauce to a gentle simmer.
Step 4: Carefully add the broken lasagna noodle pieces directly into the simmering sauce. Stir gently to ensure all noodles are submerged and separated. Reduce heat to medium-low, cover, and cook for 15-20 minutes, or until noodles are tender, stirring occasionally to prevent sticking.
Step 5: While the noodles are cooking, prepare the ricotta mixture: In a medium bowl, combine ricotta cheese, egg, 1/4 cup Parmesan cheese, and 1/4 cup chopped parsley. Mix until well combined.
Step 6: Once the noodles are tender, uncover the skillet. Drop spoonfuls of the ricotta mixture evenly over the top of the lasagna. Sprinkle generously with shredded mozzarella cheese.
Step 7: Cover the skillet again and continue to cook on medium-low heat for another 5-10 minutes, or until the mozzarella cheese is melted and bubbly. Remove from heat and let rest for 5 minutes before serving.
Step 8: Garnish with additional fresh parsley and Parmesan cheese, if desired. Serve hot and enjoy your One-Pan Stovetop Lazy Lasagna!