Preheat oven to 325°F. On a large platter, stir together flour, salt, and pepper. Dust the roast with the seasoned flour, then shake excess off.
In a heavy ovenproof skillet or Dutch oven, heat the oil over medium heat until hot
Slowly and gently add the roast and brown about five minutes, then turn the roast and brown for five minutes, then turn again and brown the roast until all of it is browned. Remove the roast from the pan and set aside.
Add the chopped onions to the drippings in the pan and sauté them over medium heat until softened. Return the roast to the skillet and add bay leaves, thyme, water, and coffee. Bring to a simmer, stirring and turning to combine the seasonings with the roast. Cover and place the skillet in the oven. Roast for 2 1/2 hours, then add the mushrooms and carrots. Continue cooking another 1/2 hour to 1 hour or until the roast is fork tender and the carrots are soft.
While vegetables are cooking along with the roast, cook any noodles or grains you’d like to serve with the roast. When roast is done, remove from the skillet and discard any bones or gristle. Set the roast aside, loosely covered with aluminum foil.
Taking the same skillet used to cook the roast and place over medium heat. Skim off fat from skillet. Add water as necessary, so that you have about 21/2 cups of liquid. Sprinkle flour over the gravy and cook for about five minutes, stirring until smooth and thickened. Stir in butter, and season to taste with salt and pepper.
Remove the foil and return the roast to the skillet to warm in the gravy
Serve immediately with buttered flat noodles, brown rice, potatoes or your favorite grains.