Place rack in center position of oven. Preheat oven to 350°F. Grease a 2-quart baking dish or spray with nonstick cooking spray. Add the chicken/turkey and ham to the baking dish and set aside.
In a medium saucepan set over medium-high heat, melt the butter. Add the garlic and sautee until fragrant. Add the flour and and cook for 1 to 2 minutes until bubbly but not brown, whisking continuously. Gradually stir in the milk, rapidly stirring until smooth. Bring to a simmer and cook, whisking continuously, for a 2 to 3 minutes until the sauce is thickened. Remove the saucepan from the heat. Stir in the salt, garlic powder, mustard powder, nutmeg and pepper. Then whisk in the cheese, ¼ cup at a time. Stir the cheese until completely melted before adding the next ¼ cup. Pour the sauce over the chicken/turkey and ham in the baking dish and toss and stir to coat.
Combine the breadcrumbs and remaining grated cheese in a medium bowl. Sprinkle over the casserole. Evenly drizzle the butter over the breadcrumbs. Bake, uncovered, for 30 minutes or until golden brown and bubbly. Allow to sit for a few minutes before serving. Sprinkle with fresh parsley, if desired.