French Onion Croque Madame

Preheat oven to 375°F.
 
Heat a skillet over medium-low and add the butter to foam. Add onions, season with salt and pepper, and add bay and thyme. Caramelize onions about 30 minutes then deglaze the onions with sherry. Add stock and let reduce until just a few spoonfuls of stock remain; keep warm.

 
In a saucepot, warm milk. In another pan, melt butter over medium to medium-high heat. Whisk in flour and cook 1 minute then whisk in warm milk. Bring to a bubble and season with salt, pepper and nutmeg. Let thicken to coat a spoon then remove from heat and stir in Dijon. 
 
To make the sandwiches, arrange bread slices on a baking sheet and top with some onions, 2 slices of ham, some of the sauce and top with cheese. Bake to brown and bubbly.

Cook eggs in butter up or over-easy, whichever you prefer. Top sandwiches with an egg and serve.