Cook beef in a large nonstick skillet over medium-high, stirring to crumble, until browned, about 5 minutes. Transfer to a 5- to 6-quart slow cooker. Add mushrooms, onion, bell pepper, and garlic, and stir to combine. Add stock, tomatoes, tomato paste, oregano, salt, and black pepper; stir to combine. Cover and cook on low 6 hours.
Stir lasagna noodles into soup, making sure to submerge all noodles in liquid. Cover and cook on low until noodles are al dente, about 30 minutes. Stir in half-and half.
Divide soup evenly among 8 bowls. Top evenly with mozzarella and basil.