Prepare the Beef: Cut the beef brisket across the grain into cubes. Pat dry with a paper towel and season with salt.
Sear the Beef: Heat the oil in a Dutch oven over medium-high heat. Brown the beef on all sides until deep golden brown. Work in batches if necessary to avoid overcrowding the pot. Remove the beef and set aside.
Cook the Vegetables: In the same pot, add the diced onion, garlic, celery, carrots, thyme, and rosemary. Cook until the onions are soft and translucent, scraping up the browned bits from the bottom of the pot.
Thicken the Stew: Stir in the flour and tomato puree, cooking for a couple of minutes to eliminate the raw flour taste and blend the flavors.
Combine Ingredients: Return the beef to the pot. Pour in the ale, beef stock, and Worcestershire sauce. Add the bay leaf and bring to a high simmer. Scrape the bottom of the pot once more to incorporate all the browned bits.
Simmer: Reduce the heat to low, cover the pot, and let the stew gently simmer for about 4 hours, or until the beef is tender and falling apart.
Serve: Remove the bay leaf before serving. Enjoy your stew with crusty bread or mashed potatoes.