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1
To roast the turkey, preheat the oven to 425F.
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2
Rub the entire breast with 4 tablespoons butter and season with salt and pepper.
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3
Place in a small roasting pan and roast for 15 minutes.
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4
Reduce the heat to 350F and continue roasting the turkey until a thermometer inserted into the center registers 155F, 1 to 1 1/2 hours.
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5
Remove from the oven, tent loosely with foil, and let rest for 10 minutes before slicing.
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6
To make the sauce, put the milk in a small saucepan and bring to a simmer over low heat.
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7
Melt the remaining 2 tablespoons butter over medium-high heat in a medium saucepan.
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8
Whisk in the flour and cook for 1 minute.
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9
Gradually whisk in the hot milk.
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10
Bring to a boil and cook, whisking constantly, until thickened and the raw flour taste has cooked out, 4 to 5 minutes.
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11
Stir in more milk if the sauce is too thick to pour.
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12
Remove from the heat and whisk in the cheddar and Parmesan cheeses, whisking until the cheddar has melted.
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13
Season with the nutmeg and salt and pepper to taste.
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14
Keep warm.
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15
To make the sandwiches, whisk together the eggs and milk in a medium baking dish.
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16
Season with salt and pepper.
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17
Dip each slice of bread in the mixture and let sit until completely soaked through, about 10 seconds per side.
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18
Heat 1 tablespoon of the butter and 1 tablespoon of the oil in a large nonstick saute pan over medium-high heat.
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19
Working in batches, cook 2 slices of the bread at a time until golden brown on both sides, about 2 minutes per side.
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20
Repeat with the remaining butter, 3 tablespoons oil, and bread.
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21
Preheat the broiler.
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22
Put the tomatoes on a rimmed baking sheet, brush with the remaining 2 tablespoons oil, and season with salt and pepper.
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23
Broil until slightly charred and just cooked through, 3 to 4 minutes.
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24
Place 4 slices of the egg bread on a baking sheet, slide under the broiler, and heat just to warm through, 20 seconds on each side.
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25
Repeat with the remaining bread.
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26
Top each slice of bread with 2 to 3 slices turkey.
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27
Ladle sauce over the top and divide the cheddar and Parmesan over the top of each slice.
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28
Place under the broiler and cook until bubbly and the tops are golden brown, about 2 minutes.
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29
Remove from the oven, top each slice with 2 slices of bacon and a tomato slice, and sprinkle with parsley.