Croque Monsieur with Mornay Sauce

FOR THE SAUCE:
Melt butter in heavy medium saucepan over medium heat. Add onion and pinch of salt. Saute until onion is tender and translucent, about 5 minutes. Add flour and stir 3 minutes (do not brown). Gradually whisk in milk. Add bay leaf. Simmer until sauce thickens, stirring occasionally, about 5 minutes. Season with salt and pepper. Cool to lukewarm, about 30 minutes. Gradually add cheese and stir until completely melted. Remove Mornay sauce from heat. Lightly beat egg yolk in small bowl. Whisk 1 tablespoon of Mornay sauce into egg. Fold egg mixture into Mornay sauce. Cover to keep sauce warm.

FOR THE SANDWICHES:
Spread 1/2 tablespoon butter over one side of each bread slice. Place 4 bread slices on work surface, buttered side down. Divide half of cheese among bread slices. Place ham slices atop cheese, dividing evenly. Top with remaining cheese. Top sandwiches with remaining 4 bread slices, buttered side up.

Heat griddle or cast iron skillet over medium heat. If using a griddle, cook sandwiches until bottom is golden brown and cheese is melted, about 3 minutes per side. If using a cast iron skillet, cook sandwiches until golden brown, about 3 minutes. Turn sandwiches over, then place skillet in 400 degrees F. oven, until golden brown on bottom and cheese is melted, about 5 minutes.

Place sandwiches on a heatproof plate or baking sheet. Spoon 1/4 cup sauce over each sandwich. Broil until sauce is pale golden and bubbles, about 2 minutes. Serve immediately.