In a Dutch oven or large saucepan over medium high heat, cook the ground beef, mushrooms, and onion until the beef is browned and the vegetables are tender, about 5 minutes. Drain well.
Stir in garlic until fragrant, about 30 seconds. Stir in chicken broth, water, tomato paste, oregano, and basil. Bring to boil.
Add the broken spaghetti in small handfuls at a time, stirring constantly (if you don't stir enough, the noodles may get stuck together). Return to boiling and reduce heat.
Simmer uncovered, stirring frequently, until spaghetti is al dente and the sauce has thickened, about 17 to 20 minutes. Season to taste with salt and pepper and garnish with the grated Parmesan cheese. Serve immediately.
Notes
4 cups of water may be substituted for the 32 ounces of chicken broth (but you'll get the best results if you use chicken broth).
Since the noodles are cooked in the sauce and they never come out, they will continue to cook. You'll want to pull the noodles as soon as they are al dente and serve this dish immediately. However, I've eaten the pasta 30 minutes after I pulled it off the stove, and it was still good! The noodles did not break down, they just didn't have the same "bite" al dente noodles have.