Preparation

Make the stock

• Position a rack in the center of the oven and heat the oven to 350°F. Roast the crabs in a large roasting pan, stirring once or twice, until bright red, about 30 minutes.
• Let the crabs cool briefly in the pan. Use a meat mallet or the edge of a sturdy mixing spoon to break the crabs into medium pieces. Pour 1 cup of hot tap water into the pan and scrape up the browned bits from the bottom and sides; set aside.
• Melt the butter in a heavy-duty 8-quart stockpot over medium-high heat. Add the celery, onion, and carrot and cook, stirring occasionally, until golden, about 8 minutes. Turn the heat down to medium, add the tomato paste and cook, stirring constantly, until a shade darker, about 2 minutes. Stir in the wine. Add the crabs and their liquid, the bay leaves, and 2 quarts cool water.
• Bring to a boil, then turn the heat down to maintain a simmer; simmer uncovered for 45 minutes, skimming any foam from the surface and replenishing with water as the liquid evaporates to maintain the level.
• Strain through a fine-mesh strainer, pushing on the solids. If not using right away (see Make-Ahead Tips, below), cool completely before refrigerating or freezing.

Make the bisque

• Melt the butter in a 6-quart Dutch oven over medium-high heat. Add the garlic and cook, stirring, just until it begins to color, about 20 seconds. Add the onions and celery and cook, stirring occasionally, until the vegetables are very soft, about 7 minutes.
• Add the bread and stir to coat. Add 1 cup of the crab stock and cook, stirring, until the bread cubes are pasty, about 1 minute. Gradually stir in another 4-1/2 cups of the stock. Add the cauliflower, 1 Tbs. salt, and 1/8 tsp. pepper. Bring to a rolling boil, then turn the heat down and slowly simmer, stirring occasionally and skimming off any foam, until the cauliflower is very tender, about 15 minutes.
• Remove from the heat, and working in batches, purée the bisque in a blender until smooth. Wipe out the pot.
• Return the bisque to the clean pot, stir in the cream, thyme, and parsley, and bring to a simmer over medium-high heat. Stir in the Brie. Adjust the heat to maintain a gentle simmer and cook, stirring and scraping the bottom of the pan to prevent sticking, until the cheese melts, 6 to 7 minutes.
• Use your fingers to break 1/2 lb. of the crabmeat into small pieces; stir it in. Cook until the crab is heated through, about 2 minutes. Adjust the consistency of the bisque to your liking by adding more broth or cooking it a little longer to thicken it.
• Serve garnished with the remaining crabmeat and chives.

Make Ahead Tips

The crab stock can be refrigerated for up to 1 day or frozen for up to 3 months.

The bisque may be made two days ahead; refrigerate it and the reserved crabmeat separately. Reheat the bisque over medium heat, stirring frequently, and garnish with the reserved crabmeat and chives just before serving.