Season beef generously with salt and pepper. In a large heavy pot, heat oil over medium-high heat until hot. Add half the beef and sauté, turning occasionally, until brown on all sides, about five minutes. Transfer to a plate and repeat with remaining beef. Remove beef from the pot and set aside.
Add mushrooms, onions and celery to the pot. Cook, tossing occasionally, until the liquid released by the mushrooms has evaporated and the vegetables just start to brown, about 7 minutes. Add garlic and cook, stirring, for 1 minute.
Return beef to the pot. Add 12 cups of chicken broth, carrots, thyme, bay leaves, 1½ teaspoons salt and ½ teaspoon pepper. Bring to a boil. Lower to a simmer and cook, uncovered, for 1 hour and 45 minutes.
Add potatoes and buckwheat. Turn the heat up and bring the soup to a boil. Turn it back down to a simmer and cook for 20 minutes.
Add the broccoli and simmer for 5-10 minutes more. If you want to thin the soup, add more chicken broth and heat through. Season soup to taste with salt and pepper. Ladle into bowls and serve hot.