01 -
Preheat the oven to 375 degrees F. Grease a 9x13-inch baking dish or line a rimmed baking sheet with parchment paper.
02 -
Whisk the eggs, milk, salt, and pepper. Melt 1 tablespoon butter in a skillet over medium-low heat, add the eggs, and stir until softly set but still moist, 3-4 minutes. Transfer to a plate to cool for 5 minutes.
03 -
Lightly flour the counter and roll the pizza dough into a rectangle about 10x14 inches. If it springs back, rest it for 5 minutes, then roll again.
04 -
Spread the cooled eggs over the dough, leaving a 1-inch bare strip along one long edge. Add the ham, cheddar, and green onions if using.
05 -
Roll the dough tightly from the filled long edge toward the bare edge. Pinch the seam to seal, then slice into 8 even rolls with a serrated knife.
06 -
Arrange the rolls cut-side up in the prepared dish. Stir the melted butter, Dijon, garlic powder, and parsley, then brush over the tops. Bake for 22-25 minutes, until golden and cooked through.
07 -
Let the rolls rest for 5 minutes before serving. Sprinkle with extra parsley if you like.