1. Heat oil in a 5 1/2- to 6-quart heavy pot over medium. Add mushrooms, onions, pepper, garlic, and salt; cook, covered, stirring occasionally, until soft (15 minutes).
2. Push vegetables aside, add beef, and cook, turning meat occasionally, until brown. Push beef aside. Add paprika, flour, and caraway; cook, stirring (1 minute). Gradually whisk in broth, then tomato paste; bring to a simmer, whisking. Stir vegetables and meat back into sauce.
3. Cover and simmer over low until meat is tender (1 1/2 hours). Stir in dill or parsley. Serve.