1. Preheat the oven to 325°F., with a rack positioned in the lower third of the oven. In a large flameproof casserole or Dutch oven, heat 2 tablespoons of the oil over high heat. Add enough meat to cover the bottom without crowding; sprinkle with salt and pepper to taste. Sauté, tossing occasionally with a wooden spoon, until well browned on all sides, 5 to 6 minutes. Transfer to a plate and brown the remaining meat in batches, adding oil as needed. Lower the heat slightly if the meat is sputtering violently. Set the meat aside on a plate.
Add the onions, carrots, garlic, and pepper flakes to the casserole, tossing to coat with the oil (add a little more oil if the pan is dry). Lower the heat to medium and sauté, tossing, until the vegetables are softened and lightly golden, about 12 minutes. Sprinkle the flour over the vegetables and cook over medium heat, stirring with a wooden spoon, until the flour is blended in and lightly browned,3 to 5 minutes.
Add a little of the Guinness to the pan; stir and scrape up all possible browned bits from the bottom with a wooden spoon, stirring them into the liquid (Deglazing Basics). Stir in the tomato paste. Return the meat to the casserole, adding enough Guinness to come nearly up to the level of the solids. Meanwhile, tie the thyme, parsley sprigs, bay leaf, allspice berries, star anise, and cloves in a piece of cheesecloth. Tuck the cheesecloth bag into the stew.
Bring the mixture to a boil. Cover the casserole tightly with foil and then with the lid. Place in the lower part of the oven; immediately lower the heat to 300°F. Bake (oven braise), stirring occasionally, until the beef is tender, about 2 hours (start checking the meat after about 1½ hours). Check occasionally as the stew bakes; if it is boiling rather than simmering, immediately lower the heat further to 250° or 275°, so you maintain a gentle simmer. Boiling will toughen the meat.
Remove the casserole from the oven. If you have time, uncover and let the mixture cool to room temperature, then refrigerate, covered, overnight. The next day, lift off all possible solidified fat from the surface with a skimmer or a metal spoon. Bring the casserole to a simmer over medium heat. Remove and discard the spice bag, gently squeezing it to release all possible juices. Taste and correct the seasonings, adding salt, black pepper, and/or red pepper flakes if needed.
Heat the remaining tablespoon of oil in a nonstick large skillet over medium-high heat. Add the quartered mushroom caps and sprinkle with salt and pepper to taste. Let the mushrooms sizzle for a moment or two. Then sauté, tossing frequently, until lightly golden, about 5 minutes longer. Add the chopped parsley and toss to combine; spoon the mushrooms over each portion of stew and serve hot.