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1
Prepare an outdoor grill for medium heat.
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2
Line a baking sheet with parchment paper.
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3
Heat the oil in a large nonstick skillet over medium-high heat.
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4
Add the sausage, and cook, stirring and breaking up with a wooden spoon, until browned and cooked through, 8 to 10 minutes.
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5
Remove from the heat, and use a slotted spoon to transfer the sausage to a plate.
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6
Reserving 2 tablespoons of drippings in the skillet (drain or add oil as needed), return it to medium-high heat.
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7
Whisk in the flour, and cook, whisking frequently, until the mixture becomes loose and turns a light tan color, 1 to 2 minutes.
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8
Slowly whisk in the milk, 1/2 teaspoon pepper and 1/4 teaspoon salt.
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9
Simmer, whisking frequently, until the sauce has thickened to the consistency of thin gravy, 6 to 8 minutes.
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10
Return the cooked sausage to the skillet, and stir.
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11
Remove from the heat, cover and set aside.
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12
Divide the pizza dough into 4 balls.
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13
Dust a clean flat work surface with flour, and roll each ball into an 8-inch circle.
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14
Transfer the dough circles to the prepared baking sheet, and brush both sides with oil.
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15
Lightly oil the grill grates.
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16
Grill the crusts until they start to puff and distinct grill marks appear on the underside, about 1 minute.
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17
Flip.
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18
Evenly divide the Cheddar among the crusts, leaving a small well in the center of each.
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19
Immediately crack 1 egg into each well.
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20
Grill, covered, until the whites have completely set and the Cheddar has melted, 8 to 10 minutes.
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21
Meanwhile, reheat the sausage gravy if needed.
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22
Remove the pizzas from the grill, and drizzle each with a couple spoonfuls of warm gravy.
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23
Garnish with the scallions.
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24
Serve immediately with hot sauce and any remaining gravy served on the side.
