Remove and discard the green leaves from the cauliflower. Cut away the florets, reserving the core. Cut off and reserve the stems. Cut the florets in pieces that measure about 1 inch. (You should have 4-5 cups florets.)
With a paring knife, cut away and discard the tough exterior of the core, then cut the core into small pieces and place them in a food processor, Add the reserved stem trimmings and pulse until very finely shopped, just short of a puree. (You should have about 1 cup; if you don™t, puree enough of the florets to make 1 cup.)
Meanwhile, bring a large saucepan of water to boil. Season the water with salt and the vinegar. (The acid in the vinegar helps keep the cauliflower white.) Add half the cauliflower florets and blanch for 2 minutes. Remove with a strainer or slotted spoon, drain well, and place in large bowl. Repeat with the remaining florets: blanch, drain, and add to the bowl. Set the saucepan aside. Season the florets with salt to taste.
Add the butter and shallots to the saucepan, place over medium heat, and cook gently for 1 to 2 minutes, or until the shallots are translucent. Season with salt and pepper and add the bay leaf, thyme, and parsley. Add the minced cauliflower and 2/3 cup water and cook gently for 5 to 6 minutes, or until most of the moisture has evaporated and the cauliflower is tender. If all the water evaporates before the cauliflower is tender, add more.
Add the cream, bring to a simmer, and simmer for 2 minutes. Remove from the heat and discard the thyme, bay leaf, and parsley. Pour the mixture into a blender and let it cool for 5 minutes.
Add the horseradish to the blender and pulse at the lowest speed to release the heat, then increase the speed and puree until smooth. Add the curry powder and blend at high speed for about 15 seconds. Toss the puree with the cauliflower florets adnd season with nutmeg, salt, and pepper to taste.
Transfer the cauliflower to an 8-inch round gratin dish or individual gratin dishes. The cream should come about halfway up the florets. Refrigerate for at least 30 minutes, or up to a day to allow the flavors to mature.
Preheat the oven to 450.
Sprinkle the gratin(s) with the cheese and breadcrumbs. Place in the oven to cook for about 15 minutes, or until it is bubbling and the center is warm. You can test it by inserting a metal skewer into the center of the gratin and touching it to your lower lip: it should feel hot. Remove the gratin(s) from the oven and turn the broiler on. Brown the top of the gratin(s) and serve.