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To make the sauce: Melt the butter in a saucepan set over medium-high heat., Add the flour, stirring to incorporate. Slowly pour in the milk, stirring constantly, until a thick sauce forms., Bring to a gentle simmer then add the cheese, stirring until it melts., To make the sandwiches: Spread the warm sauce on one side of half the bread slices., Top the sauce with a slice of ham, then a slice of cheese., Spread the Dijon mustard on one side of the remaining slices of bread, and place them mustard-side-down onto the cheese., Heat an electric panini griddle or skillet over medium-high heat., Spread the top of the sandwich with butter, and place it butter-side down onto the hot surface., Spread butter on the other side of the bread, then close the griddle or cover the pan with a lid., Toast the sandwich for 3 to 5 minutes on one side, flip it over, and toast for another 3 to 5 minutes until it's as golden as you like. Remove from the pan, and serve warm.