Heat olive oil in a large stockpot or Dutch oven over medium heat. Season steak with salt and pepper, to taste. Working in batches, add steak to the stockpot and cook, stirring occasionally, until evenly browned, about 6-8 minutes; set aside.
Add onion, carrot and celery. Cook, stirring occasionally, until tender, about 3-4 minutes.
Add garlic and mushrooms, and cook, stirring occasionally, until tender and browned, about 3-4 minutes.
Whisk in flour and tomato paste until lightly browned, about 1 minute.
Stir in wine, scraping any browned bits from the bottom of the stockpot.
Stir in beef stock, thyme, bay leaves and steak. Bring to a boil; reduce heat and simmer until beef is very tender, about 30 minutes.
Stir in sweet potatoes; simmer until potatoes are just tender and stew has thickened, about 20 minutes. Remove and discard thyme sprigs and bay leaves. Stir in parsley; season with salt and pepper, to taste.*
Serve immediately.
