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1
Place a large cast iron skillet in the oven and preheat oven to 450u00b0F (230u00b0C). Meanwhile, using a
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2
, make about 7 vertical cuts in each bagel, making sure not to cut all the way through.
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3
In a medium bowl, whisk together milk, egg, mustard, and 1 pinch nutmeg. Season with salt and pepper. Soak each bagel in the batter for 1 minute, then turn and soak the other side for 1 additional minute; make sure the custard seeps into the slits. Lift soaked bagels and let excess batter drip off, then transfer to a parchment-lined baking sheet.
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4
Cut Swiss cheese slices to sizes that will fit inside the bagel slits. Wrap each cheese slice in an appropriately sized piece of ham. (Depending on how large they are, you may need to cut the slices of ham into halves or thirds to get them to the right size.) Wedge a ham-wrapped piece of cheese into each bagel slit.
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5
Remove cast iron skillet from oven and add butter. Allow to melt and foam, swirling pan so butter evenly coats the bottom, then add bagels, bottom side down. Transfer to oven and cook until cheese is melted and bagels and ham are browning in spots, about 10 minutes.
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6
Remove pan from oven. Switch oven to broiler mode and place oven rack in top position. Pour Mornay sauce all over the tops of the bagels, then cook under broiler until browned and charred in spots, about 4 minutes, checking frequently to make sure they don't burn. Serve.
