Drizzle olive oil into Dutch oven over medium heat. Add beef to the Dutch oven and brown. Once browned, remove and place in large bowl. Pour juices from the Dutch oven into a separate small bowl.
Add flour, salt, and pepper to beef, tossing to coat. Return to Dutch oven over medium heat, turning occasionally until browned well. Pour red wine, reserved meat juices into the Dutch oven until meat is covered, plus about 1-inch. Add mushrooms, garlic, onions, tomato paste, and thyme. Stir until well-combined and allow to reach a simmer.
Place in oven and allow to cook for two hours.
Remove from oven and serve.
Notes
While the recipe calls for using burgundy or other red wine, if you prefer, you can also use beef stock in place of the wine.