Heat oil in a large, heavy skillet over medium heat. Add onions; cook and stir until tender, about 10 minutes. Transfer to a bowl.
Cook and stir beef in the same skillet until browned, 1 to 2 minutes per side. Sprinkle flour, marjoram, thyme, and pepper over beef. Pour red wine and beef broth into the skillet; stir well. Reduce heat to low and simmer until beef is tender, 1 1/2 to 2 hours.
Stir onions into the skillet. Add mushrooms. Cook, stirring, until mushrooms are tender and sauce is thick and dark brown, about 30 minutes.
Substitute olive oil for the vegetable oil if desired.
Add beef broth and wine (1 part broth to 2 parts wine) as needed in step 2 to keep beef barely covered.
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