In a large skillet, brown the onion and mushrooms in the butter. Deglaze with the Worcestershire and soy sauces and continue cooking for 1 minute. Season with salt and pepper.
Set aside and keep warm.
In a bowl, dissolve the cornstarch in the milk. Set aside.
In a small saucepan over medium heat, melt the butter with the flour, whisking continuously. Cook for 1 minute. Add the milk mixture and bring to a boil over medium heat, stirring constantly. Add the cheeses and stir until melted. Cover, set aside and keep warm.
Preheat the grill, setting the burners to high. Oil the grate.
In a bowl, combine the meats. Season with salt and pepper. Shape into 8 large, thin patties (see note).
Grill the patties for 2 to 3 minutes on each side, or until they are cooked through. Toast the buns.
For each burger, spread cheese sauce on the bottom half of the bun, then layer with a patty, some mushrooms, a second patty, lettuce, bacon and pickles. Close with the top half of the bun.
To make the job easier, place the patties between two sheets of plastic wrap and flatten them by pressing down on the plastic by hand, or use a hamburger press.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.