Dice the onion and mince the garlic. Cook both in a large pot with the olive oil over medium heat for 2-3 minutes, or until they begin to soften. Add the ground beef and continue to cook until the beef is fully browned.
Add the chili powder, cumin, oregano, diced tomatoes, and diced green chiles (do not drain the tomatoes or chiles). Stir to combine with the beef.
Add the noodles and beef broth. Stir to combine and push the noodles down until they are mostly submerged under the broth. Place a lid on the pot and allow it to come up to a simmer. When it begins to simmer heavily, turn the heat down slightly (just above low) and allow it to continue simmering for 10 minutes. Stir every few minutes to keep the pasta from sticking to the bottom of the pot.
After about ten minutes the pasta should be fully cooked and most of the broth absorbed. If it is still slightly watery, let it continue to cook for a minute or two without the lid. Taste the pasta and if it is not spicy enough for you, add the cayenne pepper.
Drain the can of black olives and stir them into the pasta. Add the cheese and stir it in until it is fully melted. Slice the green onions, sprinkle over top, and serve.