Place escargots in a small bowl, and cover with cold water; set aside for 5 minutes. This will help to remove the canned flavor they may have.
Preheat oven to 350 degrees F (175 degrees C). Lightly grease an 8x8 inch baking dish.
Drain the water from the escargots and pat dry with a paper towel. Melt butter with the garlic in a large skillet over medium-high heat. Add the escargots and mushroom caps; cook and stir until the mushroom caps begin to soften, about 5 minutes.
Whisk together wine, cream, flour, pepper, and tarragon in a small bowl until the flour is no longer lumpy. Pour this into the skillet, and bring to a boil. Cook, stirring occasionally until the sauce thickens, about 10 minutes.
Remove the skillet from the heat, and use a spoon to place the mushrooms upside down into the prepared baking dish. Spoon an escargot into each mushroom cap. Pour the remaining sauce over the mushroom caps and into the baking dish. Sprinkle grated Parmesan cheese overtop.
Bake in preheated oven until the Parmesan cheese has turned golden brown, 10 to 15 minutes.
