- Béchamel Sauce: In a small heavy bottomed saucepan, melt the butter. Once it starts to bubble and foam add the flour and whisk for 30 seconds, stirring continuously. Add the warm milk and continue to stir until completely smooth. Salt and pepper to taste. Set aside.
- Sandwich: Spread the Dijon mustard on one side of each piece of bread. Top 2 pieces of bread with even amounts of the ham, cheese and tarragon. Then place the other two pieces of bread on top to make the sandwiches. Reserve some of the tarragon to chop and serve as garnish on the sandwich.
- In a large fry pan melt one tablespoon of butter. Add each sandwich and lightly brown on both sides.
- Place the sandwiches on a sheet pan and top with the béchamel sauce. Top each with the grated Gruyere and place under the griller until golden brown and bubbly. Serve immediately.
Note: Another version of this recipe is Croque Madame, which is the same sandwich but topped with a fried egg.