Heat the olive oil in a large pot over medium heat. Add the ground beef and cook until browned, breaking it up with a spoon as it cooks. Drain excess fat if needed.
Add the chopped onion, minced garlic, and sliced mushrooms to the pot. Cook for 5 minutes until the vegetables soften.
Sprinkle the flour over the mixture and stir for 1 minute to coat everything evenly.
Pour in the red wine and scrape the bottom of the pot to loosen any browned bits. Let it simmer for 2 minutes.
Stir in the tomato paste, beef broth, sliced carrots, cubed potatoes, and dried thyme. Season with salt and black pepper.
Bring the stew to a boil, then reduce the heat to low. Cover and simmer for 25 minutes until the potatoes and carrots are tender.