For the béchamel: Heat the milk, cream, and salt together in a microwave or in a saucepan on the stovetop until warm. Slowly melt the butter in a saucepan, and once melted, add the flour and stir until combined. Slowly whisk in the warm milk and cream and bring the béchamel to a simmer. Once thickened and bubbling, add the Worcestershire sauce and 1/2 cup of the cheddar cheese; stir to combine. Chill in the refrigerator.
To assemble the sandwiches: Preheat the broiler.
Spread a teaspoon or so of the béchamel on both sides of the bread slices. Place 2 slices of Gruyère and 2 slices of duck bacon on one side of the sandwich. Close the sandwich and do the same for the other three.
In a frying pan, using a small amount of butter, toast each side of the sandwich as you would a grilled cheese.
Mix together the cheddar and the Parmesan in a small bowl. Place the toasted sandwiches on a baking sheet and spread liberally with the béchamel covering the entire slice, doing the same with a handful of the shredded cheese. Place the baking sheet under your broiler and cook for 2 to 4 minutes, until the top of the sandwich is bubbling and the cheese becomes a golden brown.
In a small saute pan, cook each egg sunny-side up with a little butter; the yolks should stay runny. Place one egg on top of each sandwich. Serve with a dash of Worcestershire sauce and cracked black pepper.
From JACK’S WIFE FREDA: Cooking from New York’s West Village by Maya and Dean Jankelowitz. Recipes by Julia Jaksic. Published by Blue Rider Press, an imprint of Penguin Publishing Group, a division of Penguin Random House LLC. Copyright © 2016 by NoamBennyLLC