Heat the olive oil in a Dutch oven. Brown the pot roast on all sides in the hot oil; remove from pan and set aside. Cook the onion and garlic in the hot oil until they begin to soften and turn brown, about 5 minutes. Add the carrots, mushrooms, and potatoes to the pot; cook and stir until they begin to color, 2 to 3 minutes. Mix the flour into the vegetables; stir continuously for 1 minute. Pour the beef stock and beer into the mixture and bring to a boil, stirring continuously. Add the Bay leaf, thyme, brown sugar, mustard, tomato paste, salt, and pepper. Place the pot roast atop the entire mixture. Cover pot with lid.
Bake in the preheated oven until the meat and vegetables are completely tender, about 2 1/2 hours.
