Heat a dutch oven over medium high heat, add the ground beef, olive oil, garlic, & onions and stir everything together, breaking the meat up as you go- cooking until the meat is browned and cooked through. Drain, and return the mixture to the pot.
Stir in the water, broth, both tomatoes, Italian seasoning, and bay leaves. Lower the heat, bringing the mixture to a simmer. Cover, and let cook for 20 minutes, stirring occasionally.
Stir in the pasta, cover, and continue simmering an additional 30 minutes- stirring occasionally, until the pasta's cooked through.
Remove the bay leaves, and salt & pepper, to taste. Stir in the mozzarella cheese until evenly combined.
Serve immediately, scooping into bowls, and topping with the shredded cheddar.