Begin by cutting the roast into approximately 2 inch pieces.
Heat a Dutch oven over medium heat and add the olive oil.
In a mixing bowl, combine flour, salt, and pepper.
Place the beef chunks into the dry ingredients to cover all surfaces with a light coating.
Sear the beef in the hot skillet. Do not overcrowd the pot to prevent steaming rather than searing. Once the beef chunks are seared, remove them and place on a clean bowl. Tent the bowl with foil to prevent moisture loss from the meat.
Melt the butter in the Dutch oven and add onions, garlic, celery, and carrots.
Sauté the vegetables for about 5 minutes or until the onions are slightly golden and tender.
Stir in the flour and continue cooking for 1-2 minutes.
Pour in the entire pint of Guinness Extra Stout into the Dutch oven and scrape the bottom to try to incorporate any brown bits into the mix.
Carefully to prevent splattering, return the beef chunks and juices from the bowl into the Dutch oven.
Add the beef broth and tomato paste and stir to combine.
Add the thyme, rosemary, bay leaf, salt and pepper.
Cover the Dutch oven, reduce the heat to low, and simmer for 2-2½ hours. Stir every half hour.
Remove the cover, add the peas, stir, and continue to simmer uncovered for 45 minutes to 1 hour longer.
Serve this thick, tender stew in a large bowl with a warm slice of Irish soda bread.