Heat olive oil in a large Dutch oven over medium-high heat. Brown the ground beef for 5-7 minutes, breaking it apart as it cooks, then drain excess fat if needed and set aside.
In the same pot, sauté diced onion for 3 minutes until softened, then add minced garlic and cook for 1 minute more. Stir in sliced mushrooms and cook for 4-5 minutes until they release their moisture and begin to soften.
Return the browned ground beef to the pot with mushrooms and onions. Add beef broth, diced tomatoes with juice, egg noodles, thyme, oregano, salt, and black pepper—stir everything thoroughly to combine.
Bring the hearty ground beef casserole crowd mixture to a simmer, then cover and reduce heat to medium-low. Cook for 12-15 minutes until noodles are tender and most liquid is absorbed, stirring occasionally.
Stir in the shredded cheddar cheese and green beans, mixing until cheese melts completely and beans are distributed throughout the dish. Taste and adjust seasonings as needed.
While the casserole finishes, melt butter in a small bowl and combine with breadcrumbs. Sprinkle this mixture evenly over the top of the beef casserole.
Transfer to a preheated 375°F oven and bake for 8-10 minutes until breadcrumbs turn golden brown. Let rest for 5 minutes before serving.