Bacon, Egg, and Cheddar Breakfast Pizza

Remove the dough from its packaging. Coat a medium bowl with 1 teaspoon olive oil, add the dough, turn to coat, and cover. Let stand at room temperature for 30 minutes, until pliable and no longer refrigerator-cold. Meanwhile, position an oven rack in the lower third and preheat the oven to 475°F. Shred the cheddar and finely chop the chives.

While the dough rests, arrange the bacon in a cold skillet and place it over medium heat. Cook for 8 to 10 minutes, turning occasionally, until fully cooked, browned, and crisp. At the same time, melt 1 tablespoon butter in a small saucepan over medium heat. Whisk in 1 tablespoon flour and cook for 1 minute. Gradually whisk in 12 tablespoons milk, then add 1/4 teaspoon salt and all the black pepper. Simmer, whisking frequently, for 2 to 3 minutes, until smooth and thick enough to coat a spoon. Remove the sauce from the heat.

Transfer the bacon to the paper towel-lined plate. Once cool enough to handle, crumble it into bite-size pieces. Carefully pour the bacon grease into a heatproof container and let it cool completely before discarding it. Wipe out the skillet with paper towels held in tongs.

Coat the rimmed baking sheet with the remaining 2 teaspoons olive oil. Dust a clean work surface with the remaining 1 tablespoon flour. Press and gently stretch the rested dough into an approximately 11-by-15-inch rectangle. Lift it with both hands, transfer it to the prepared baking sheet, and press it toward the corners, leaving a slightly thicker 1/2-inch border. Par-bake on the lower oven rack for 6 minutes, until puffed, set on top, and just beginning to color. Remove it from the oven and gently press down any large bubbles with the spatula. Keep the oven at 475°F.

Whisk the white sauce briefly, then spread it evenly over the crust, leaving the raised border exposed. Sprinkle with 3 ounces cheddar, followed by the crumbled bacon. Return the pizza to the lower oven rack and bake for 7 minutes.

While the pizza bakes, whisk the eggs with the remaining 1 tablespoon milk and 1/4 teaspoon salt. Melt the remaining 1 tablespoon butter in the wiped skillet over medium-low heat. Add the eggs and cook for 2 to 3 minutes, gently folding with a spatula to form soft curds. Transfer the eggs to a clean plate while they are still glossy and slightly underdone; they will finish cooking on the pizza.

Remove the pizza from the oven. Distribute the softly scrambled eggs over the bacon and sprinkle with the remaining 3 ounces cheddar. Bake for 3 to 5 minutes, checking at 3 minutes, until the crust edges and underside are well browned, the cheese is completely melted and bubbling, and the thickest portions of egg register 160°F on an instant-read thermometer. Remove the pizza promptly once the eggs reach 160°F so they remain tender.

Sprinkle the pizza with the chives and let it rest for 3 minutes. Cut into 8 pieces and serve 2 pieces per person.