Preheat the oven to 400 degrees F. Butter a glass 9 by 13-inch baking dish and set aside.
In a medium saucepan, melt 4 tablespoons of the butter over medium heat. Add the flour and cook, stirring constantly, until thickened into a pale blond roux, 2 to 3 minutes. Add the hot stock in a steady stream, whisking to incorporate. Bring to a simmer and cook, stirring frequently with a heavy wooden spoon until thick. Add 1/4 teaspoon of the salt and 1/8 teaspoon of the pepper, and stir to incorporate. Slowly whisk in the cream and simmer, stirring, until well incorporated and thickened. Remove from the heat and very lightly film the top with the milk to prevent a skin from forming.
In a large saute pan or skillet, heat the remaining 2 tablespoons of butter over medium-high heat. Add the diced chicken, season lightly with Essence, and cook, stirring, until lightly browned and cooked through, about 4 minutes. Remove with a slotted spoon. To the fat and juices in the pan add the shallots and garlic and cook, stirring, for 1 minute. Add the mushrooms, remaining 1/4 teaspoon salt and 1/8 teaspoon pepper, and cook, stirring, until they have given off their water and are starting to color, 3 to 4 minutes. Add the ham and cook, stirring, for 1 minute. Add the sherry and bring to a boil, stirring to deglaze the pan. Add the tarragon and green onions, and return the chicken to the pan. Stir well to blend and cook until the sherry has evaporated. Reduce the heat to low and stir in enough of the cream sauce to bind and thicken, 1 to 1 1/2 cups. Remove from the heat and let cool slightly.
Place the crepes on a work surface. One at a time, spoon the filling along the bottom third of each crepe, about 3 tablespoons per crepe, and roll into a cylinder to enclose the filling. Place, seam side down, in the prepared baking dish. Repeat with the remaining crepes.
To the remaining cream sauce, add the Gruyere and stir to incorporate. Spoon the sauce evenly over the crepes. (NOTE: The crepes can be tightly covered with plastic wrap and refrigerated for 1 day or frozen for 3 days at this point. Bring to room temperature before baking.)
Bake until warmed through and the top starts to become bubbly, 15 to 20 minutes. Remove from the oven and top with the Parmesan. Bake until the cheese is melted and the topping is golden brown, 5 to 10 minutes.
Remove from the oven and place in a chafing dish holder or on trivets. Serve hot, 1 to 2 crepes per person.
Essence (Emeril's Creole Seasoning):
Yield:About 2/3 cup
Combine all ingredients thoroughly and store in an airtight jar or container.
Recipe from "New New Orleans Cooking", by Emeril Lagasse and Jessie Tirsch. Published by William and Morrow, 1993.
Whisk together the flour, eggs, milk, and 4 1/2 teaspoons of the butter to form a smooth, thin batter. Refrigerate for at least 1 hour before proceeding.
Heat a heavy 6-inch skillet or crepe pan over medium-high heat. When hot, brush with a light coating of the remaining butter. Ladle about 1/4 cup of crepe batter into the pan, tilting the skillet to evenly coat the pan with batter. Cook until golden brown on the bottom and the top begins to look dry, 1 to 2 minutes. Using a spatula, carefully turn the crepe and cook on the second side just until the bottom colors slightly, about 30 seconds. Transfer to a plate and cover loosely with waxed paper to keep warm. Repeat with remaining batter.
Assemble as directed in the Creamy Chicken and Mushroom Crepes. (Alternatively, make ahead and when cool, layer between sheets of waxed paper and wrap tightly in plastic wrap. Refrigerate until ready to use, up to 3 days.)