Preheat the oven to 400 degrees F. and line a baking sheet with parchment paper.
In a small saucepan on medium-low heat, add the milk and allow it to heat to a simmer.
In a separate medium saucepan on low heat, add the butter and once melted add the flour.
Stir the butter mixture continuously until doughy and cooked thoroughly, for about 2 minutes.
Slowly and carefully whisk the hot milk into the butter mixture.
Whisk continuously until thick and smooth. Add the Parmesan and ½ cup Gruyere cheese until melted.
Line the bread slices on the prepared baking sheet and place into the oven to toast. Bake for 5 minutes before turning to bake for an additional 2 minutes.
Lightly brush half of the slices of toast with Dijon mustard, top the mustard with a slice of ham, followed by half of the remaining Gruyere cheese.
Top each with the remaining slices of toast and generously spread a layer of the white sauce on top of each sandwich followed by the remaining Gruyere cheese.
Turn the oven broiler on low and place the baking sheet bake into the oven until the cheese is golden and bubbly.
Remove from the oven and serve while hot.