Put meat in freezer for 30 minutes for easier slicing. Slice meat into thin strips about 2 inches long. Sprinkle with pepper. Heat oil a large, heavy skillet over medium-high heat, swirling to coat bottom. Saute mushrooms until tender, 2 to 3 minutes. Transfer to a plate. Saute onion in same skillet until brown, 3 to 4 minutes. Add to mushrooms. Add meat to skillet and brown quickly on all side rare, 2 to 3 minutes for tenderloin, 3 to 5 minutes for round steak or sirloin. Add to mushrooms. Add flour to skillet. Gradually pour in broth, whisking constantly. Cook over medium-high heat for 2 to 3 minutes, or until thickened, whisking constantly. Reduce heat to low. Whisk in remaining ingredients except sour cream. Stir in mushrooms, onions, and meat. Cook for 15 minutes. Pour sour cream in a small amount of meat mixture. Add sour cream mixture to skillet and cook for 5 minutes, or until heated through, stirring occasionally.
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