1Prepare a medium-hot fire in your grill with a large cast-iron grill griddle on the grill grates. Close the grill lid.
2Divide the dough into 4 portions. On a floured surface, pat or roll each portion into 6- to 8-inch-diameter circle.
3Toss the greens with 2 tablespoons of olive oil in a bowl until they glisten
4Sprinkle a pizza peel or a flexible cutting board with half of the cornmeal. Arrange a pizza circle on the cornmeal-dusted peel.
5Hold the pizza peel level with the grill rack so that the dough round will slide onto the center of the hot grill griddle. With a quick forward jerk of your arm, slide the dough round from the peel to the stone. Quickly slide a second pizza circle onto the grill griddle. Close the lid and let grill-bake for 2 to 4 minutes, or until the crusts is browned on the bottom and firm.
6Turn the pizza crusts with tongs and brush quickly with olive oil. Dot with half of the green onion and bacon lardoons, Create a circle of frisée in the center of each pizza.
7Crack an egg onto each pizza. Drizzle the egg with olive oil. Cover and grill for 2 to 4 minutes, or until the egg is cooked to your liking. Adjust the seasoning to taste. Repeat the process with the other pizzas.