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1
Preheat a waffle iron to medium-high.
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2
Preheat the oven to 200 degrees F. Whisk together the flour, Gruyere, ham, Parmesan, baking powder, sugar, 1/4 teaspoon salt and a few grinds of pepper in a large bowl.
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3
Whisk together the milk, butter, oil, 1 egg and the scallions in another bowl.
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4
Pour the milk mixture into the flour mixture and gently stir until just incorporated (it's okay if there are some lumps).
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5
Lightly brush the top and bottom of the waffle iron with butter.
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6
Fill the waffle iron about three-quarters of the way full (some waffle iron should still be showing).
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7
Close the lid gently and cook until the waffles are golden brown and crisp, 6 to 7 minutes.
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8
Keep the cooked waffles warm in the oven or covered with foil on a plate while you make the remaining waffles.
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9
Lightly brush the waffle iron bottom with more butter.
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10
Crack the remaining 4 eggs right onto the waffle iron and keep the iron open (do this in batches if your iron isn't large enough).
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11
Sprinkle the eggs with salt and pepper.
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12
Cook until the whites are set and the yolk is still runny, 4 to 5 minutes.
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13
Serve 1 egg on each waffle, using a spatula to transfer.
