Rinse mushrooms; trim off and discard discolored stem ends. Cut mushrooms vertically into 1/8- to 1/4-inch slices. In a 10- to 12-inch nonstick frying pan, combine mushrooms, onion, and 2 tablespoons butter. Stir often over high heat until juices have evaporated and mushrooms are lightly browned, about 10 minutes. Add brandy and stir until liquid has evaporated, about 1 minute. Remove from heat and stir flour into mushroom mixture. Then stir in mustard, catsup, horseradish, and beef broth.
Return pan to high heat and stir until mixture is boiling, about 3 minutes. Add 1 cup sour cream and stir to blend. Add salt and pepper to taste. Pour mushroom sauce into a bowl.
Rinse meat and pat dry. Cut across the grain into 1/8-inch-thick slices. Rinse and dry frying pan, place over high heat, and add remaining tablespoon butter. When it just begins to brown, add half the beef; stir until meat is lightly browned in some places and still pink in others, 2 to 3 minutes. With a slotted spoon, transfer cooked meat to mushroom sauce. Add remaining beef to pan and repeat to brown. When all the meat is cooked, return stroganoff mixture to frying pan and stir until bubbling, 2 to 5 minutes.
Pour stroganoff into center of pasta ring, top with a dollop of sour cream, and sprinkle with dill. Cut through pasta with a sharp knife and serve stroganoff and pasta with 2 large spoons.