With the rack in the highest position, preheat the oven to broil.
In a saucepan over medium-high heat, sauté the mushrooms, green onions and celery in the butter until they begin to brown. Add the garlic and thyme and stir to combine. Deglaze with the cognac or brandy.
Add the cream of mushroom soup and the milk. Stir to combine. Add the turkey meat and bring to a boil. Season with salt and pepper. Pour into an 11 x 7-inch (28 x 18 cm) baking dish. Cover with the cheese.
Bake under the broiler for 3 to 5 minutes or until the cheese is nicely golden.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.