Preheat an oven to 450°F or preheat a broiler.
Heat the bechamel in a small pot and whisk in 60g/2 oz of gruyere and 60g/2 oz of emmental cheese until smooth. Allow it to cool while prepping other ingredients.
Slice the brioche in one inch slices.
Place a heavy gauge skillet or cast iron pan over low heat. If you have the ability to heat the pan to a specific temperature 315°F works beautifully.
Assemble the sandwich but layering like this; Bread, mustard, sliced emmental, ham, sliced emmental, mustard, and bread. This will help keep everything from falling out.
Gently brush the exterior of the bread with neutral flavored oil. Do not put butter on this sandwich, the brioche will absorb the butter and make the bread soggy. We control this by adding an extremely small amount of oil to the outside.
Place the sandwich in the dry pan and allow it to cook. This will take about 2 minutes per side.
Scoop about 2-3 oz of the bechamel on top of the sandwich and spread it to the edges.
Top each sandwich with a large portion of the gruyere (about 90g/3oz) and place the entire pan in the oven on the bottom rack for 2-3 minutes. The residual heat from the pan will continue to crisp the bottom of the sandwich.
Once the sandwich has heated through, move it to the top of the oven near the broiler. Watch the broiler to make sure the sandwich doesn’t burn.
Optional; use a searzall to create the perfect crust if you don’t have a broiler.
At this point this sandwich is ready to eat. The final step to turn this Croque monsieur (Crispy Mister) into a croque madame (Crispy Misses) is to add a poached egg. We like to poach an egg in reduced ham stock but you can poach an egg in any liquid you want.
To poach an egg heat the ham demi-glace or poaching liquid to 185°F and crack the egg into the liquid. Cook the egg for 2-3 minutes depending on the doneness you prefer.
Remove the egg and place it on top of the sandwich and serve immediately.