Brown the ground beef. Heat a large cast iron skillet over medium-high heat. Add the ground beef and cook for 6–8 minutes, breaking it into small pieces, until nicely browned. If there is a lot of excess grease, spoon some of it off. Add the chopped onion and all 2 tablespoons of butter. Cook for another 4 minutes, stirring occasionally, until the onion softens.
Add the garlic and flour. Stir in the minced garlic and cook for about 30 seconds, just until fragrant. Sprinkle the flour over the beef mixture and stir well. Cook for 1–2 minutes to remove the raw flour taste.
Make the beef gravy. Slowly pour in the beef broth, stirring and scraping up the browned bits from the bottom of the skillet. Add the Worcestershire sauce, dried thyme, salt, and black pepper. Bring to a gentle simmer and cook for 5–7 minutes, stirring occasionally, until the gravy thickens.
Cook the egg noodles. Meanwhile, bring a large pot of salted water to a boil. Cook the egg noodles according to the package directions until just al dente. Reserve 1/3 cup of the pasta cooking water, then drain the noodles.
Combine the noodles and gravy. Stir the reserved pasta water into the beef gravy until smooth. Add the drained egg noodles and gently toss until well coated. If the gravy is too thick, add a little more pasta water as needed.
Finish and serve. Warm everything together for about 1 minute, then sprinkle with freshly chopped parsley. Serve hot while the noodles are tender and the gravy is rich and silky.