Season meat with salt and pepper. Heat oil in a large skillet over medium high heat. Add beef and cook about 4 minutes, stirring to brown evenly. Remove and set aside.
Melt butter in the skillet. Add onions and cook until softened, stirring occasionally, about 4 minutes. Add mushrooms and cook about 4 minutes more. Sprinkle 1 tablespoon flour into skillet and stir until incorporated. Repeat with second tablespoon of flour. Pour in broth in a stream while stirring. Bring to a boil, then reduce heat and stir in mustard.
Return beef and any accumulated juices. Heat for about 2 minutes. Remove from heat and add sour cream.