Preheat the oven to 375 degrees. Coat a 9x13-inch baking dish with non-stick cooking spray.
In a medium bowl, whisk together the milk, water, eggs and vanilla.
In a separate bowl, gently toss together the diced ham, turkey, 1 1/2 cups Swiss cheese, and parsley.
In a small bowl, combine the sliced strawberries and strawberry topping or jam.
Cut the French toast into 3/4-inch cubes. Layer half of the French toast cubes into the prepared baking dish, top with half of the meat and cheese mixture; repeat. Pour the milk and egg mixture over all. Top with remaining 1/2 cup Swiss cheese. Let stand 10-15 minutes before baking OR overnight in the refrigerator and bake in the morning.
Bake for 30-35 minutes, until the casserole is golden and the center is set. Rest for 5-10 minutes. Dust with confectioners' sugar and top with strawberries sauce.