Heat a third of the butter and 1 tablespoon of the oil in a frying pan and brown the meat briskly in batches, without overcrowding the pan. Transfer the browned beef to a casserole.
Add a little more butter and oil to the pan and fry the onions until lightly browned. Scoop into the casserole. Finally fry the button mushrooms and add those to the casserole too.
Pour the Guinness into the frying pan and bring to the boil, scraping in the brown residues from frying. Stir in the tomato puree and sugar.
Pour the Guinness mixture into the casserole, add enough hot water to come about 3/4 of the way up the meat and add the bouquet garni, salt and freshly ground pepper.
Cover and transfer to the oven. Cook for 2-3 hours or until the meat is very tender. Check occasionally, giving it a stir, and if necessary add a little more hot water.
Remove the stalks from the shitake mushrooms and discard. Slice the caps thickly. Heat the remaining butter in a frying pan and sauté the mushrooms, then stir into the casserole and return to the oven for 5 minutes.
Discard the bouquet garni, adjust the seasoning and serve.