In a large pot over medium-high heat, heat half the oil. Place the beef cubes in a large bowl and toss with flour, half the salt, and pepper.
Add to the pot and cook, turning occasionally, until browned on 2 sides, about 4 to 5 minutes.
Reduce the heat to medium. Add in the chopped onion, stirring occasionally, until just tender, about 5 to 7 minutes. Add ¾ of the beef broth. Bring the mixture to a boil over medium-high heat. Then, reduce the heat to medium-low, cover the pot, and simmer until the beef is tender enough to shred with a fork, about 2 to 2 ½ hours.
Pour the remaining beef broth into the pot and bring it to a boil. Add the egg noodles and cook, stirring occasionally, until they are tender, about 7 to 8 minutes. Season with salt as needed.
Divide the beef and noodles mixture evenly among two bowls. Serve topped with lots of freshly ground black pepper.