1. Fit the grill with the griddle plates and preheat with the upper plate set to 450°F and the lower plate set to 350°F. Press the SEAR button for the upper plate only.
2. Brush the bottom side of the bread with the softened butter. Spread 1 teaspoon of the Dijon/aioli on the top of each piece of the bread. Top with the ham and then Gruyère, evenly divided between the two sandwiches.
3. Once the grill has preheated, place the assembled sandwiches on the lower plate and setting the cover height adjuster on the highest notch, close the upper plate until it is sitting just above the Gruyère. Let the sandwich cook until the cheese is fully melted on top, about 8 to 10 minutes. Note: As the cheese melts down, you can lower the upper plate a notch or two to get the best results.
4. Remove sandwiches from the grill. Pour about 1 to 2 tablespoons of béchamel over each one and serve immediately for Croques Monsieurs.
5. If you wish to make this into a croque madame, after removing the sandwich, fry two eggs on the hot griddle plate and place one on top of each sandwich, then top with the béchamel.
3 tablespoons unsalted butter
2 tablespoons unbleached, all-purpose flour
1½ cups whole milk
2 pinches sea or kosher salt
pinch ground nutmeg
1. Melt the butter in a saucepan placed over medium heat. Once the butter melts, stir in the flour and cook over medium heat while stirring occasionally, about 3 minutes.
2. Whisk in the milk a little at a time so that mixture is smooth and homogenous. Turn heat to medium-high and bring the sauce to a heavy simmer. Reduce heat and gently simmer until sauce thickens and coats the back of a spoon. Continue to whisk the sauce while heating to ensure it does not burn on the bottom.
3. Remove from heat and season with salt and nutmeg.