In a large pot over medium-high heat, heat 2 tablespoons oil. Place beef in a large bowl and toss with flour, 2 teaspoons salt, and ½ teaspoon pepper.
Add half of beef to pot and cook, turning occasionally, until browned on 2 sides, 4 to 5 minutes. Transfer beef to a plate; repeat with remaining 2 tablespoons oil and beef.
Reduce heat to medium. Cook onion and ½ teaspoon salt, stirring occasionally, until just tender, 5 to 7 minutes. Return beef to pot and add 6 cups broth. Bring to a boil over medium-high heat. Reduce heat to medium-low, cover, and simmer until beef is tender enough to shred with a fork, 2 to 2 ½ hours.
Transfer beef to a large plate and shred with 2 forks into bite-size pieces.
Pour remaining 2 cups broth into same pot and bring to a boil. Add noodles and cook, stirring occasionally, until tender, 7 to 8 minutes. Return beef to pot, toss to combine, and season with remaining 1 ½ teaspoons salt as needed.
Divide beef and noodles among bowls. Serve topped with lots of pepper.
