Heat oven to 325°F Heat 1 tbsp olive oil in a large, hot, ovenproof casserole dish. Brown the beef on both sides in the hot dish, in batches if applicable, making sure beef is well browned; if it sticks a little, leave it until it releases. Remove from pan and add another 1 tbsp oil. Brown bacon, then add the vegetables and mushrooms, cooking for about 5 minutes each addition. Add the bouquet garni and cook for an additional 1-2 minutes.
Add the tomato puree and the wine. Bring to a boil and boil hard for about 10 minutes to reduce a little. Add stock, return the meat to the pan, and bring back to a boil. Season to taste with salt & pepper, then cover and cook in the oven for 3 hours or until the meat is tender.
Remove the meat to a plate. Strain the liquid and return to the pan. Reserve the bacon and vegetables, but discard the bouquet garni. Bring to a boil and boil until reduced to about 1-1 1/4 cups. Cut the meat into big chunks. Slide the bacon and vegetables into the sauce, followed by the meat, and simmer gently for 5-10 minutes until piping hot.
When meat is close to done, make the pommes purée. Peel the potatoes and cut into even-sized dice, then cook for about 12-15 minutes in boiling salted water. Drain well, then return to the pan and cook for 1-2 minutes over medium heat with no liquid added (to dry the potatoes). Mash the potatoes thoroughly or press them through a potato ricer back into the pan - they should be very smooth and lump-free. Don't use a food processor, as it will make the potatoes gluey.
Gradually beat the butter into the potato puree until it starts to look shiny. Heat the milk and cream in a small pan until on the point of boiling, then slowly mix into the potato purée with some salt and freshly ground pepper. Potatoes should be very creamy in consistency.
Serve the boeuf bourguignon over the potato puree.
Excellent with a glass of the same wine used in cooking and with a fresh, crisp salad on the side.