Breakfast Stromboli

Heat the oil in a medium nonstick pan over medium heat until shimmering. Add the sausage and onion and cook, breaking up the meat with a wooden spoon into small pieces and stirring occasionally, until the sausage is cooked through, about 8 minutes. Meanwhile, place the 4 eggs and the salt in a medium bowl, season with pepper, and whisk to combine.

Reduce the heat to medium-low. Pour in the egg mixture. Using a rubber spatula, scramble the eggs, stirring occasionally and pushing the cooked parts from the edges of the pan to the center, until they are almost set but not dry, about 3 minutes. Transfer to a large plate and spread into an even layer to cool while the oven is heating (the eggs will continue to set).

Arrange a rack in the lower third of the oven and heat to 425°F. Make the egg wash by beating the remaining egg and water in a small bowl together; set aside. Line a baking sheet with parchment paper; place the parchment on a work surface.

When the oven is ready, roll the pizza dough out into a rough 12x14-inch rectangle. Transfer it onto the parchment. Position the parchment with the dough on it so a short end is facing you. Sprinkle 1/2 of the cheese lengthwise down the center of the dough, creating a strip of cheese that is 12 inches long and 3 1/2 inches wide, leaving a 1-inch border at each short end and a 4 1/4-inch border on each long end. Spoon the egg mixture evenly over the cheese. Sprinkle with the remaining cheese and parsley.

Using a very sharp small knife or pizza cutter, cut 1 1/2-inch-wide strips on either side of the filling (as if you were making a thick fringe on either side of it), stopping the cut about 1/4-inch from the filling.

Starting with the bottom left strip, fold it up and over the filling at a slight angle. Next, fold the bottom right strip up and over the filling, meeting and slightly crossing the first strip, making a sort of crisscross or chevron pattern. Continue alternating left and right strips so you wind up with a crisscross that covers most of the filling. Press the dough strips together firmly without squishing the filling so the strips stay together when baked.

Seal the stromboli by pinching together the uncovered ends and the strips closest to them. Grasping the parchment, transfer the stromboli and parchment onto the baking sheet. Liberally brush a layer of the egg wash on the stromboli.

Bake until the stromboli is golden-brown, about 20 minutes. Let the stromboli cool for 5 minutes before cutting crosswise and serving.