In a small bowl, stir together sour cream and dillweed; set aside.
In a large skillet, cook beef, half at a time, in hot oil over medium-high heat until desired doneness. Remove beef from skillet and set aside. Add onion and garlic to the same skillet; cook for 8 to 10 minutes or until onion is tender.
Meanwhile, cook noodles according to package directions, adding broccoli for the last 3 minutes of cooking; drain well.
Return noodles and broccoli to pan; cover and keep warm.
Sprinkle flour over onion mixture in skillet. Stir to coat. Add broth, tomato paste, and Worcestershire sauce. Cook and stir until thickened and bubbly. Cook and stir for 1 minute more.
Return all beef to skillet; heat through. Season to taste with pepper. Remove from heat. Stir in sour cream mixture. Serve beef mixture on top of noodles and broccoli.
Makes 4 servings.
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