Heat half of the butter and half of the oil in a large frying pan. Add the shallots and fry until they are just beginning to brown, then tip in the pancetta and fry until lightly browned. Transfer to a plate with a slotted spoon.
Place the pieces of beef in a polythene bag with the seasoned flour. Shake until well coated, then remove and shake off any excess. Add to the frying pan and fry until lightly golden on all sides. Transfer to a casserole dish with a lid.
Add a little of the red wine to the frying pan, scraping the bottom to release any sediment. Then pour over the top of the beef in the casserole dish, along with the rest of the wine, the stock, carrots, celery, bay leaves and thyme. Add the sautéed shallots and pancetta and season to taste. Stir to combine, cover and simmer gently for 1 1/2 hours or until the meat is tender but still holding its shape.
Halfway through cooking, heat the remaining oil and butter in a large frying pan and cook the mushrooms until just tender and lightly browned, stirring. Add the brandy and cook for another few minutes, then stir into the casserole dish and return to the oven for the remaining cooking time.
When the boeuf bourguigon is ready, season to taste and serve with crusty bread.