Preheat oven to 325ºF / 160ºC

Place bacon in a Dutch oven or a large heavy kettle over low heat, and cook until fat is rendered. Remove solid pieces with a slotted spoon, and set aside. Note: If you don't want to use bacon, just melt 2 tablespoons butter. Raise heat to medium-high. Season beef lightly with salt but generously with pepper and lightly toss with flour. Place half the cubes in the pan. Cook in a single layer (don't crowd the pan, do it in more batches if necessary) over medium-high heat until well browned on all sides, then transfer to a large bowl. Repeat with remaining beef, adding the second batch of browned beef to the bowl.

If the pan is dry, add 2 tablespoons butter. Add onions and cook until softened but not brown, about 10-12 minutes. Add garlic and cook for 1 minute. Add brandy and cook, stirring, until the bottom is deglazed and any crusted-on bits come loose. Add stock, thyme, bay leaves, smooth Dijon mustard and coarse mustard. Whisk to blend, then return meat to pot. Bring liquid to a gentle simmer, cover pot and place in the oven. Cook until meat is very tender, about 1 1/4 hours, stirring occasionally.

Stir in carrots and shallots, and continue cooking for 35-40 minutes, or until vegetables are tender. As they cook, heat 2 tablespoons butter in medium skillet over medium-high heat, and sauté mushrooms until browned and tender. Stir mushrooms and reserved crumbled bacon into stew, then taste, and adjust seasoning.

Serve hot, with boiled potatoes or buttered egg noodles.