Cut away florets and reserve the core. Cut off and reserve stems, and cut florets into about 1 inch pieces. Cut away tough exterior of the core, and then cut the core into small pieces. Place in food processor; add reserved stem trimmings and pulse until very finely chopped, just short of a puree. You should have about one cup. If you don't, then puree some of the florets to get one cup. Blanch florets in a pot of salted water with a little vinegar, for 2 minutes, shock in an ice water bath, drain and dry. Season the florets with salt to taste. Add butter to pan and sweat shallots until translucent, then add minced cauliflower, thyme, bay leaf and parsley, and 2/3 cup water and cook cauliflower until tender. Add the cream and bring to a simmer for 2 minutes. Remove from heat and discard herbs. Add to a blender and let cool for 5 minutes. Add horseradish and puree. Toss florets with puree, and season with nutmeg, salt, and pepper. Transfer gratin to gratin dish, and refrigerate 30 minutes. Sprinkle with bread crumbs and cheese, and bake at 450 for about 15 minutes until it is heated through. Brown the top in the broiler and serve.