In a large 12-inch skillet over medium-high heat, add the ground beef and break it apart as it cooks. Brown until no pink remains, about 5 to 7 minutes. Drain any excess fat from the pan and return it to the heat.
Add the chopped onion, minced garlic, oregano, parsley, basil, salt, and pepper. Stir to combine and cook for about 3 minutes, until the onion softens and the garlic is fragrant.
Add the crushed tomatoes, chicken broth, and lasagne pasta. Stir everything together, making sure the pasta is submerged in the liquid as much as possible.
Bring to a boil, then reduce the heat to a low simmer. Cook uncovered for 15 minutes, stirring occasionally to prevent the pasta from sticking to the bottom of the pan. The pasta should be tender and most of the liquid absorbed when done. If the mixture looks too dry before the pasta is cooked through, add a splash of broth or water.
Stir in the shredded mozzarella and cook for another 30 seconds to 1 minute until the cheese is fully melted and the mixture looks creamy. Remove from heat and serve immediately.