Bring a large pot of lightly salted water to a boil; add penne and cook, stirring occasionally, until mostly cooked, about 8 minutes. Add broccoli; continue cooking until penne is tender, about 3 minutes more. Drain and keep warm.
Trim beef and slice into thin bite-size strips.
Heat oil in a large skillet over medium heat. Add beef, onion, and garlic; cook and stir until onion is tender and beef is browned, about 5 minutes. Remove from heat. Stir in flour, salt, and black pepper.
Return skillet to the heat. Add beef broth, tomato paste, and Dijon mustard. Cook and stir until thick and bubbly, 5 to 8 minutes. Continue cooking for 1 minute more. Remove from heat.
Divide penne and broccoli among 4 bowls. Spoon beef mixture on top.