In a shallow bowl, combine flour, salt, and pepper. Place cut chuck roast on a large plate, sprinkle the flour mixture over the beef, tossing with your hands to coat evenly in the flour. Shake off excess flour. Add two tablespoon olive oil to a dutch oven over medium-high heat. Once hot, brown the beef, working in batches, adding additional olive oil between batches. Remove browned beef to a large plate, set aside.

Once all the beef is browned, add the beef broth and red wine to the dutch oven, scrapping up the browned bits from the bottom with a large spoon. Stir in tomato paste. Return the browned beef to the dutch oven, add the bay leaves and thyme. Bring to a boil, reduce heat, cover and simmer for 1 hour, stirring occasionally.

After 1 hour, add the chopped carrots and onions to the dutch oven, continue to simmer, uncovered for ½ hour. Add the chopped mushrooms and garlic, simmer for an additional ½ hour, uncovered, or until the beef and carrots are tender. Remove the bay leaves before serving.