1. Melt the butter in a large saucepan. Add the mushrooms and cook until the liquid from the mushrooms has evaporated. Add the cognac and cook for 30 seconds. Add 1/4 cup of the cream, the salt, pepper, and herbs and bring to a boil. Add the dissolved potato starch, mix well, and boil to thicken. Remove from the heat.
2. Preheat the broiler. Drain the artichokes.
3. Whip the remaining cream until stiff. Rapidly fold into the mushroom mixture, and immediately fill the artichoke bottoms. Sprinkle with the cheese and place under the broiler for 2 to 3 minutes, until nicely browned.
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