Pat scallops dry with a paper towel and refrigerate until needed.
Set a saucepan over medium heat, and melt 2 tablespoons of the butter in it. Add the flour, and cook, stirring constantly, for 2 minutes.
Slowly add the chicken stock, whisking constantly, to create a smooth, thick sauce. Add the cream, thyme and cayenne. Heat the sauce, whisking often, until it is just about boiling then reduce heat to a simmer. Cook for 7 minutes, stirring occasionally. Remove from heat.
Put 2 tablespoons butter in a large frying or sauté pan. Place over medium heat. Melt butter then add the shallots and cook, stirring occasionally, for 3 minutes. Add the garlic and cook one minute longer. Add the mushrooms and cook, stirring often, for about 6 – 7 minutes until mushrooms are beginning to turn brown.
Add the vermouth, brandy or Cognac to the pan and cook for 1 minute. Add the mushroom mixture to the cream sauce; taste and add salt and pepper to your liking. Put in the fridge to cool; stirring occasionally, for 15 – 20 minutes.
Combine bread crumbs, parsley and grated cheese in a medium bowl. Drizzle with olive oil; stir.
Use remaining butter to grease 4 medium gratin dishes (approximately 1.5 cups/375 mL each). Divide the scallops among the dishes; top with the cream sauce, dividing evenly. Finish each dish with bread crumb mixture. Place on a baking sheet, cover dishes with plastic wrap and refrigerate for up to 24 hours.
Just before serving time, preheat oven to 400F. Remove plastic wrap from gratin dishes and place in hot oven for 18 – 22 minutes, or until tops are lightly browned and bubbling.