Place 2 tablespoons butter and 1 tablespoon olive oil in Dutch oven or large pot over low heat, and cook until butter is melted and bubbly. Then raise heat to medium and add onions 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 more olive oil to the pan. Toss 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, approx. 10 minutes per batch. Transfer beef cubes to the 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, approx 1-2 minutes. Add stock, Dijon, and grainy mustards. Whisk to blend, then return meat and onion mixture to pot. Lower heat, partly cover, and simmer gently until beef is very tender, about 45 minutes.
Add carrots and mushrooms to the pot and continue simmering for an additional one hour and 15 minutes, or until carrot slices are soft and fork-tender.
Lastly, add red wine and 1 tablespoon butter (if desired). Simmer 5 minutes, then taste, and adjust seasoning if necessary.
Serve stew right from the pot or ladle into individual bowls. Garnish with parsley if desired.