Place bacon/pancetta in a Dutch oven over low heat, and cook until fat is rendered. Remove solid pieces with a slotted spoon, and set aside. 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.

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.

Add Cognac to the empty pot, and cook, stirring, until the bottom is deglazed and the crust comes loose. Add stock, Dijon mustard and 1 tablespoon Pommery mustard. Whisk to blend, then return meat and onion mixture to pot. Lower heat, partly cover, and simmer gently until meat is very tender, about 1½ hours.

Add carrots, and continue simmering for 30 minutes, or until slices are tender. As they cook, heat 2 tablespoons butter in a medium skillet over medium-high, and sauté mushrooms until browned.

Stir mushrooms into stew. Pour wine on skillet to deglaze mushroom bits and pour into stew along with remaining mustard. Simmer 5 minutes, then taste, and adjust seasoning.