4 boneless, skinless chicken breasts (6 to 8 oz. each), tenders removed
Salt and pepper
2 tbsp. olive oil
1 cup heavy cream
½ cup grainy Dijon mustard
A few grates of nutmeg
8 slices prosciutto cotto or other mild ham
¾ lb. Gruyère, coarsely shredded (2 to 2 1/2 cups)
Finely chopped fresh chives, for garnishing
4 eggs, optional
Heat a large cast-iron skillet or griddle over medium-high, and preheat the broiler.
Working with 1 breast at a time, butterfly the chicken by cutting horizontally with a sharp knife almost all the way through. Open like a book and pound between sheets of plastic to about 1/4 inch thick. Season the chicken with salt and pepper. Add 1 tbsp. oil, one turn of the pan, to the skillet. Add 2 chicken breasts and cook until golden and cooked through, 2 to 3 minutes per side; transfer to a foil-lined baking sheet. Repeat with the remaining 1 tbsp. oil, one turn of the pan, and the remaining 2 chicken breasts.
In a small saucepan, heat the cream and mustard over medium, whisking often, until the sauce can coat a spoon, about 3 minutes; season with salt and nutmeg.
Top the chicken with the prosciutto, cream sauce and cheese. Broil until browned, about 3 minutes. Garnish with the chives.
For croque madames, heat a large nonstick skillet over medium. Melt a large pat of butter, crack in the eggs and cook until the whites are almost set, about 3 minutes. Flip and cook until over-easy to over-medium. Set on top of the croque monsieur and garnish with the chives.