Put the beef in a medium bowl. Season with the flour, salt and pepper and stir until coated. Set aside.
Add the oil to large stock pot and heat on high until hot. Turn down to medium-high and add the beef, searing all sides (4 to 5 minutes). Remove the beef from the pan and set aside. Add the onions and 1 cup of beef broth to the pot and deglaze, scraping bits off the bottom of the pot, stirring and cooking onions for 2 minutes. Add the garlic and cook 1 additional minute.
Add the beef, 1 cup beef broth, 2 bottles Guinness, thyme sprigs and bay leaves. Heat to a gentle boil, then turn down, cover with a lid and simmer for 2 hours. Skim fat, remove bay leaves and thyme sprigs and discard.
Add the carrots, celery, water, tomato paste freshly chopped thyme, salt and pepper. Increase heat to medium-low until the stew reaches a soft, gentle boil and let it simmer 45 minutes to 1 hour, uncovered, so the sauce will reduce and thicken. Remove from heat and serve.