In a small skillet, cook the bacon until crisp; drain on paper towels.
In a large skillet, melt the butter over medium heat and whisk in the flour. Cook, stirring, until the flour turns amber brown, 3 to 4 minutes. Whisk in the milk and continue cooking, whisking constantly, until the sauce thickens, about 5 minutes. Remove the pan from the heat, whisk in the 4 tablespoons of Parmesan and season with salt and the pepper. Taste the sauce and add more pepper if desired.
Preheat the broiler. For each sandwich, place 2 slices of toast in 2 ovenproof dishes. Cover the 4 slices of toast with the turkey slices and top generously with cheese sauce and grated Parmesan. Place the sandwiches under the broiler and cook until the sauce bubbles and begins browning, 2 to 3 minutes. Remove from the oven and arrange 2 pieces of bacon in an X across the top of each open-faced sandwich.