Melt butter in a saucepan over medium heat.

Stir in flour and cook for about 3 minutes, stirring occasionally, until fragrant.

Season with salt and pepper.

Gradually add cream and milk, stirring continuously until the mixture thickens, about 10 minutes.

Temper the egg yolks by slowly whisking in 3 tablespoons of the hot cream mixture, one tablespoon at a time.

Pour the egg yolk mixture back into the saucepan and stir to combine.

Remove from heat and stir in the Parmesan cheese until melted and smooth.

Preheat broiler.

Arrange toasted bread slices on a baking sheet.

Top each slice with turkey, tomato slices, and Gruyere cheese.

Generously spoon the white sauce over each sandwich.

Broil until the sauce is bubbling and the cheese is melted, about 5 minutes.

Top each sandwich with 2 slices of cooked bacon.