In a large pot or Dutch oven over medium-high heat, brown the ground beef with the diced onion, breaking up the meat as it cooks, about 6-8 minutes. Drain excess fat if needed. Add garlic and cook for 1 minute more.
Stir in tomato sauce, diced tomatoes with their juices, beef broth, soy sauce, Italian seasoning, and paprika. Bring mixture to a boil.
Add the elbow macaroni, stir well, and reduce heat to medium-low. Cover and simmer for 15-18 minutes, stirring occasionally, until pasta is tender and has absorbed most of the liquid.
Remove from heat and stir in half of the shredded cheddar cheese. Serve topped with remaining cheese.