Preheat oven to 350 degrees F. Cook pasta according to package directions; drain. Return pasta to hot saucepan; cover to keep warm.
Place roast on a cutting board; reserve juices. Using two forks, pull meat apart into bite-size pieces; set aside.
Remove stems and gills from mushrooms; coarsely chop mushrooms. (You should have about 4 cups.) In a 12-inch skillet cook mushrooms, onion, and garlic in hot butter over medium heat for 4 to 5 minutes or until tender. Stir in flour and tomato paste. Add beef broth, reserved meat juices, Worcestershire sauce, paprika, salt, and pepper. Cook and stir until thickened and bubbly. Remove from heat.
Add pasta and beef to mushroom mixture in skillet; stir to combine. Transfer meat mixture to a 3-quart casserole or rectangular baking dish. Bake, covered, for 30 minutes or until heated through. If desired, sprinkle with parsley.
Meanwhile, in a small bowl combine sour cream, horseradish, and dill. Spoon some of the mixture over each serving.