Prepare the seasoned flour. In a small bowl, combine 2–3 tablespoons flour with a pinch of salt and black pepper.
Coat the beef. Pat the beef pieces dry with paper towels. Lightly coat them with the seasoned flour, shaking off any excess.
Brown the beef. Heat olive oil in a large, heavy-bottomed pot over medium heat. Add the beef in batches and brown on all sides, turning with tongs. Avoid overcrowding the pot so the meat browns rather than steams.
Add the garlic. Stir the minced garlic into the browned beef and cook for approximately 1 minute, until fragrant.
Add the liquids. Pour in the beef stock, Guinness stout, and red wine. Stir gently, scraping the bottom of the pot to loosen any flavorful browned bits.
Add the seasonings. Stir in the tomato paste, sugar, dried thyme, Worcestershire sauce, and bay leaves.
Simmer the stew. Bring the mixture to a gentle boil, then reduce the heat to low. Simmer for approximately 2 hours, stirring occasionally, until the beef begins to become tender. Add a little additional beef stock or water if the liquid reduces excessively.
Prepare the vegetables. While the beef simmers, melt the butter in a large frying pan over medium heat.
Brown the vegetables. Add the potatoes, diced onion, and carrots. Cook for approximately 30 minutes, stirring occasionally, until the vegetables become tender and develop some golden-brown color. Leave the pan uncovered so the vegetables brown instead of steaming.
Combine the vegetables and stew. Carefully add the browned vegetables to the simmering beef mixture and stir gently.
Finish cooking. Continue simmering for approximately 20 minutes, or until the beef is fork-tender and the potatoes and carrots are fully cooked.
Adjust the seasoning. Remove the bay leaves. Taste the stew and add salt and freshly cracked black pepper as needed.
Serve warm. Ladle the Guinness beef stew into bowls and serve immediately, or refrigerate it for a convenient make-ahead dinner.