Dry all surface moisture from steak strips with paper towels and season with salt and pepper.
Heat 1 tablespoon butter and 1 tablespoon oil in a 12-inch heavy skillet over moderately high heat.
Add beef in 2 batches and cook, turning once, until browned on both sides but still pink inside, about 1 minute.
With a slotted spoon, transfer to a plate.
Reduce heat to medium and add remaining butter and oil.
Sauté shallots or onions with mushrooms until translucent and tender, about 8-10 minutes.
Transfer to the plate with the steak, leaving as much butter and oil in the skillet as possible.
If necessary, add butter to make about 2 tablespoons.
Blend in flour and cook until frothy, stirring.
Add beef stock in a slow stream, whisking constantly, for 2 minutes to make a roux.
Add Worcestershire sauce, salt and pepper to taste and red pepper.
Simmer and stir until thickened and smooth.
Add beef, onions or shallots and mushrooms to sauce and heat through.
Remove from heat and blend in sour cream and mustard.
Warm to serving temperature.
Serve over noodles, rice, or potatoes.
Garnish with dill or parsley.