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1
To make the bechamel, heat the milk, half-and-half, and a pinch each of salt, pepper, and nutmeg in a medium saucepan until bubbles begin to form.
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2
Keep warm over low heat.
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3
In a large saucepan, melt the butter over medium-low heat until golden.
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4
Add the flour and cook, whisking constantly, until the mixture smells nutty and toasty, about 2 minutes.
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5
Continue whisking and add the hot milk mixture in a slow, steady stream.
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6
Bring the mixture to a boil while whisking.
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7
Remove from the heat.
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8
In a small bowl, whisk the egg yolks until blended.
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9
Continue whisking and add a cup of the hot milk mixture in a slow, steady stream.
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10
Whisk the egg mixture back into the hot milk mixture until well blended.
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11
Cook over low heat, stirring constantly, until thickened.
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12
Add the cheeses and stir until melted.
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13
Season with more salt, pepper, and nutmeg to taste.
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14
Its easier to spread the sauce if refrigerated first in an airtight container until cold, but you can also use it right away.
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15
To make the sandwiches, lay your bread slices in 2 rows of 4 to form a rectangle on a large sheet of parchment paper.
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16
The edges of the bread should be touching.
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17
Dollop 2 tablespoons bechamel onto each slice of bread.
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18
Use an offset spatula or the dull edge of a butter knife to push the sauce evenly into the bread, spreading back and forth repeatedly.
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19
This will take some time; you want the bread to completely soak up the sauce.
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20
On the bottom row of bread, arrange the ham in an even layer.
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21
Dollop the remaining bechamel over the ham and spread evenly.
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22
Top with the remaining bread, bechamel side up.
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23
Sprinkle the cheeses evenly over the sandwiches and then press them into the bread.
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24
Bring up the sides of parchment to enclose the sandwiches, then wrap tightly with plastic.
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25
Refrigerate until the sandwiches hold together nicely, at least 1 hour, but preferably 1 day.
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26
The longer the bechamel sits on the bread, the moister the sandwich will be.
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27
Preheat the oven to 350F.
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28
Butter a rimmed baking sheet.
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29
Trim the crusts off the sandwiches, then slice each sandwich in half diagonally.
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30
Transfer to the prepared pan, spacing the sandwiches 1/2 inch apart.
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31
Bake until the cheeses melt and the tops are golden brown, about 10 minutes.
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32
When the sandwiches are almost done, heat a large nonstick skillet over medium-high heat.
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33
Crack the eggs into the skillet, spacing them apart, and cook just until the whites are set, about 1 minute for quail eggs, longer for large eggs.
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34
Slide the eggs on top of the sandwiches and sprinkle fleur de sel and cayenne on top.
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35
Serve immediately.
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36
To crack quail eggs, gently tap the sharp blade of a small knife against the equator of the egg.
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37
When it breaks through the shell, carefully twist the knife to split the shell in half.
