4 tablespoons room temperature Cabot Unsalted Butter, divided
2 tablespoons flour
1½ cups milk
½ teaspoon salt
1 tablespoon grated Parmesan cheese
4 thick slices “pain de mie” (firm white bread)
4 ounces Cabot 3-year Aged Cheddar, sliced
4 ounces Cabot 3-year Aged Cheddar, shredded (about 1 cup)
8 slices Black Forest ham
1 tablespoon Dijon mustard, as needed
2 large eggs
Get the ingredients you need at a convenient nearby location.
Make the Bechamel Sauce:
WARM the milk slightly in the microwave, about 15 seconds.
WARM a saucepan over medium heat and add 2 tablespoons butter. Once it is melted and bubbly, but not brown, whisk in the flour and stir continuously for 1 to 2 minutes to cook the flour slightly.
ADD the warmed milk slowly, while continuing to whisk. Whisk until the sauce thickens, about 10 minutes. Remove from the heat, stir in the salt and Parmesan cheese.
Make the Sandwiches:
ASSEMBLE the sandwiches by adding 2 ounces sliced cheese, 4 slices of ham and a 1/2 tablespoon of mustard between two bread slices. Repeat to make the second sandwich. Butter the outsides of the sandwiches on each side with the remaining two tablespoons of butter.
HEAT a skillet over medium heat and toast the sandwiches until golden on each side and the cheese is melted.
PREHEAT the oven broiler until hot, about 500 degrees F.
TRANSFER the grilled sandwiches to a sheet pan and top with the Bechemel sauce and the shredded cheese, evenly divided between the two sandwiches.
COOK the sandwiches under the broiler until bubbly and golden, about 5 minutes.
FRY the 2 eggs in a buttered skillet on medium heat, leaving yolks whole and a little soft (or cooked to your preferred doneness).
TOP each of the broiled sandwiches with a fried egg.
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