Place bacon in a Dutch oven over low heat, and cook until the fat is rendered. Use a slotted spoon to transfer to a large bowl.
1/4 lb Bacon, chopped
Raise heat, and add onion and shallots. Cook until softened but not browned, 10 to 15 minutes. Use a slotted spoon to transfer to a large bowl.
1 ea Onion, diced, 3 ea Shallots, diced
If necessary, add 2 tablespoons butter to the pot to augment fat. Dust beef cubes with flour, and season with salt and pepper. Shake off excess flour, and place half the cubes in the pot. Cook over medium-high heat until well browned, almost crusty, on all sides, then transfer to a bowl with onions. Repeat with remaining beef.
4 Tbsp Butter, 2 lbs Beef chuck, 1" cubes, 2 Tbsp Flour
Add Cognac to the empty pot, and cook, stirring, until the bottom is deglazed and the crust comes loose. Add stock and 1/2 cup of the Dijon mustard. Whisk to blend, then return the meat and onion mixture to the pot. Lower heat, partly cover, and simmer gently until meat is very tender, about 1½ hours.
1/2 cup Cognac, 2 cups Beef stock, 3/4 cup Dijon mustard
Add carrots, and continue simmering for 30 minutes, or until slices are tender.
4 ea Carrots, sliced into half-moons
Heat 2 tablespoons butter in a medium skillet over medium-high, and sauté mushrooms until browned.
1/2 lb Mushrooms, mushrooms, stemmed, cleaned and quartered
Stir mushrooms into stew along with remaining mustard and red wine. Simmer for 5 minutes, then taste, and adjust the seasoning. Serve hot.
1/4 cup Red wine