Heat oil in a large Dutch oven (4-6 qt), over high heat. Add your beef cubes and brown the meat, 3-5 min. Remove meat to a bowl and set aside.
If needed, add a little more oil. Add the onions and carrot chunks and sauté until golden, 10 min. Add the mushrooms, celery, and garlic, and sauté 2-3 min.
Reduce the heat to medium. Add tomato paste, bay, thyme, and pepper. Mix until evenly distributed.
Add the wine and deglaze the pan, scraping up any stuck bits of goodness with a flat wooden spoon.
Return the beef to the pan and simmer, 2-3 minutes to reduce the wine.
While the wine is simmering, in a small bowl, pour a little beef broth into the flour. Whisk until a smooth paste forms, then add more broth, until it is all combined and smooth. Add the broth mixture to the Dutch oven.
Bring the pot to a simmer, then reduce the heat to medium-low and simmer 45 min to 2 hours. (The longer you simmer, the more tender the meat will become.)
About 10 minutes before you are ready to serve dinner, heat 1 quart of water in a large saucepan to boiling. Reduce heat to a simmer and add cauliflower. Simmer 5 minutes, or until cauliflower is just barely tender.