Preheat a panini press. (If there are temperature settings, choose medium.)
MAKE THE BÉCHAMEL In a small saucepan, melt the butter over medium-high heat.
Add the flour and whisk to form a paste. Add the milk and whisk until the paste is dissolved.
Add the Dijon and salt and whisk until thickened.
Cook, stirring constantly, for 2 minutes; remove from the heat.
Spread ¼ cup of the béchamel over the bottom half of the croissant.
Add a sprinkling of the cheese (approximately ¾ ounce).
Top with two slices of ham and an additional sprinkling of the cheese.
Place the croissant top over the cheese and transfer to the panini press.
Cook until the cheese is melted, the ham is warmed through and the croissant has grill marks from the press, for 2 to 3 minutes. (Cooking times will vary depending on the panini press being used.) Serve immediately.