Bring a pot of salted water to a boil, then cook the egg noodles according to the package directions. Drain them when they are al dente, with a little firmness remaining in the center.

Place the ground beef and chopped onion in a skillet over medium-high heat and cook for about 10 minutes, breaking the beef into small crumbles. Listen for a steady sizzle and continue until the meat is deeply browned and the pan has browned bits on its surface.

Lower the heat to medium, then stir in the garlic, Worcestershire sauce, and Italian seasoning for 1 minute. The garlic should smell fragrant without taking on dark color.

Scatter the flour over the beef mixture and stir continuously for 1 to 2 minutes. The flour should disappear into the drippings and smell lightly toasted rather than raw.

Pour in the beef broth a little at a time while stirring and scraping the skillet bottom. Keep stirring until the flour fully dissolves and the browned bits blend into the liquid.

Simmer the gravy for 5 to 10 minutes, stirring occasionally, until it reaches your preferred thickness. The sauce is ready when it clings smoothly to the back of a spoon; add a splash more broth if it tightens too much.

Add the drained egg noodles to the skillet, toss until coated, and season with salt and pepper if needed. Serve right away while the noodles are springy and the gravy is glossy.