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Remove beef from the marinade and blot dry on paper towels. Heat the oil and butter and the remaining 4 sprigs thyme in a heavy-bottomed saucepan on a high heat. When the oil begins to smoke, remove the thyme. Add the beef and brown evenly on all sides. Season with salt and freshly ground black pepper. Strain the marinade into the beef and stir with a wooden spoon, scraping up the flavorful bits in the bottom of the pot. Add bouquet garni and beef stock. Bring to a simmer and cook, uncovered, until the liquid starts to thicken, about 15 to 20 minutes. Cover and cook on low heat for 2 hours.
After about 2 hours add the baby carrots, garden peas, and mushrooms, along with a pinch of sugar to balance out the acid from the red wine. Turn the heat up slightly and simmer, uncovered, for 30 minutes more, until the vegetables and meat are tender. Season with salt and pepper.
Garnish with chopped parsley and chives. Squeeze some of the roasted garlic onto the croutons, drizzle with extra-virgin olive oil and serve with the stew.
Put garlic on a sheet of aluminum foil. Drizzle with olive oil, and season with salt and freshly ground black pepper. Add a sprig of thyme and fold the foil around the garlic. Cook for 30 to 40 minutes or until garlic is tender and golden brown.