Heat the olive oil in a large Dutch oven over medium high heat and sear the beef on all sides until brown, working in batches to prevent over-crowding. Transfer the beef to a plate and set aside.
Add the onions to the Dutch oven and cook until lightly browned, about 5-7 minutes. Transfer to a bowl and set aside. Next brown the carrots, adding more oil if needed. Transfer the carrots to the onions and set aside.
Add the mushrooms and cook for 2 minutes. Add the wine, bring to a boil, reduce to heat and simmer for about 3-4 minutes or until the wine is reduced by half.
Return the beef to the Dutch oven along with the onions, carrots, celery, garlic, tomato paste, bay leaves, thyme, pepper and salt. Stir to combine.
In a bowl, whisk together the beef broth and flour until all the lumps are gone. Add the beef stock mixture to the Dutch oven, stirring to combine. Bring the pot to a boil, reduce the heat to low, cover and simmer for at least one hour, preferably 2 hours.
Towards the end of the cooking, boil 4 quarts of water in a large pot and cook the cauliflower florets for 6-8 minutes or until tender. Drain and keep warm until ready to use.
Divide the cauliflower between the bowls and ladle the stew over the cauliflower. Serve with a dollop of sour cream and a sprig of fresh parsley.