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1
Adjust an oven rack to the middle position and preheat to 375 degrees F. Lightly butter a 9- by 13-inch baking dish.
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2
Lay 6 slices of the bread in a single layer on the bottom of the baking dish (trim if needed).
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3
Sprinkle 2 heaping tablespoons of the gruyere on top of each slice.
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4
Then top each with 2 slices of the ham, folding the ham if needed to fit on top of the bread.
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5
Place the remaining 6 slices of bread on top of the of the ham to form 6 sandwiches.
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6
Sprinkle the remaining gruyere on top and on the sides of the sandwiches.
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7
Set aside.
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8
Whisk together 4 of the eggs, the half-and-half, cinnamon, nutmeg, 1 teaspoon salt and 1/2 teaspoon pepper in a large mixing bowl.
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9
Pour on top of the sandwiches.
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10
Use your hands to lightly press the sandwiches down into the custard.
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11
Spray a large piece of foil with nonstick spray.
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12
Place the foil, sprayed-side down, on top of the baking dish, crimping the sides of the foil around the dish.
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13
Bake for 30 minutes.
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14
Remove the foil and bake until the custard is set but still slightly jiggly, about 10 minutes.
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15
Switch the oven to broil and broil until the top is light golden brown, 3 to 5 minutes.
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16
Allow the casserole to rest at room temperature for 20 minutes.
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17
Meanwhile, heat the butter in a large nonstick pan over medium heat.
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18
Crack 3 eggs into the pan (it's ok if they stick together) and lightly sprinkle with salt and pepper.
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19
Cook until the whites start to set, 2 to 3 minutes, and then cover and continue cooking until the whites are set but the yolks are still runny, 1 to 2 minutes.
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20
Place each on top of a sandwich.
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21
Repeat with the remaining 3 eggs.
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22
Use a metal spatula to remove a sandwich with egg from the casserole and place on a serving plate.
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23
Serve with warm maple syrup for drizzling.
