Ok, so this is not really a thing (yet)- there is either a Croque Monseiur or a Croque Madame- wonderful French bistro sandwiches, which started showing up on menus around 1910- the classic Croque Monseiur has ham and gruyere- the Croque Madame adds a fried egg on top. This variation takes its inspiration from both- we make a 'butter' of grated gruyere, dijon mustard and butter, then nestle it between some wonderful french style slow cooked ham, soak our hearty but soft sourdough in egg beaten with milk, pan fry it in butter and voila! Croque Mademoiselle!
(makes two sandwiches)
Four slices of sourdough bread (I use a boule)
2-3 Tbsp. unsalted butter
1/2 cup (loosely packed) grated gruyere
2 tsp. dijon mustard (not whole grain)
6 thin slices French ham (sometimes called Jambon Blanc, slow cooked ham will also be fine)
1 Tbsp. milk or cream
Freshly cracked pepper
Melt one of the tablespoons of butter. Mix with the gruyere and mustard, this will form a paste. Spread the paste on one side of each of the slices of bread, add some freshly cracked pepper. We omit salt here because the ham and gruyere are already sufficiently salty. Place three slices of ham in each sandwich, (the sides of the bread with the gruyere spread are on the inside). Beat the egg thoroughly and mix in the milk or cream. Quickly immerse the outside of each sandwich on both sides in the egg, wiping off excess. You don't want too much egg, the flavor will overwhelm the rest of your sandwich.
Melt the remaining butter in a frying pan and at a medium to medium low heat, cook each sandwich for about 5 minutes on each side. Enjoy! This is delicious! It is also very fast and simple! If you don't care for ham, why not try turkey? If you don't care for egg, skip the egg part and have a wonderful grilled ham and cheese with a hint of dijon!