Place the cut-up chuck roast into a medium glass bowl and sprinkle it with 1/2 teaspoon of salt and 1/2 teaspoon of pepper. Add the flour and mix together until the beef is coated with flour.
Heat 2 tablespoons of olive oil into a 5 1/2 - 6 quart soup pot or dutch oven. Add the beef to the pot in batches and brown on both sides. Place the cooked beef on a plate and set it aside.
In the same pot, heat another tablespoon of olive oil and cook the onions until translucent, about 3-4 minutes. Into the onions, add in the garlic and thyme, and cook for another 2 minutes or until the garlic is fragrant.
Into the pot, with the garlic, onions, and spices, pour in the entire can of Guinness, bring to a boil, and then reduce to a simmer. Cook for about 3-4 minutes. While the Guinness is simmering scrape up the brown bits on the bottom of the pot.
Stir in the tomato paste.
Add in the potatoes, carrots, beef, beef broth, and bay leaf.
Cook uncovered for 2 hours, stirring every half hour or so.
Cover the stew and cook for another hour.
Stir in 1 teaspoon of salt and pepper.