Preheat oven to 425 degrees F. Rub entire breast with butter and season with salt and pepper. Place in a small roasting pan and roast for 15 minutes. Reduce the heat to 350 degrees F and continue roasting until an instant-read thermometer inserted into the center registers 155 degrees F, about 1 to 1 1/2 hours. Remove from the oven, loosely tent with foil and let rest 10 minutes before slicing.
Melt butter over medium heat in a medium saucepan. Whisk in the flour and cook for 1 minute. Whisk in the milk, bring to a boil and cook, whisking constantly, until thickened and the flour has cooked out, about 4 to 5 minutes. Whisk in cheese and cook until the cheese has melted. Season with nutmeg and salt and pepper, to taste.
Whisk together the eggs, milk and salt in a medium bowl. Dip each slice of bread in the mixture and let sit about 30 seconds, or until completely soaked through. Heat 2 tablespoons of butter and 2 tablespoons of oil in a large nonstick saute pan over medium-high heat. Cook 4 slices of the bread at a time until golden brown on both sides. Remove and place on a baking sheet. Repeat with the remaining bread.
Preheat broiler. Place the egg bread on a baking sheet, place under the broiler and heat on both sides for 20 seconds just to warm through. Top each slice of bread with 2 to 3 slices of turkey and 2 slices of tomato, ladle sauce over the top and divide the cheddar cheese and Parmesan over the top of each slice. Place under the broiler and cook until bubbly and the top is golden brown. Remove from the oven, top each slice with 2 slices of bacon and sprinkle each slice with chives and parsley.