In a large bowl, I combine the diced chicken, crumbled bacon, shredded mozzarella, and Caesar dressing. I season it with a bit of salt and pepper, then fold in the sliced green onions. Mixing everything before it touches the dough keeps every bite evenly flavored.
I dust my counter with flour and divide the pizza dough into two or three equal pieces, depending on how big I want each bake. Each piece gets rolled into a rectangle, roughly 7 by 12 inches, with even thickness throughout. A thin, uneven patch is where the filling will leak out later.
I spoon the chicken filling down the center of each dough rectangle, leaving a couple of inches of bare dough around the edges. Then I fold the short ends in first, followed by the long sides, pressing the seams closed like wrapping a package. Placing it seam-side down on the baking sheet keeps it sealed while it bakes.
Once all the bakes are arranged on my parchment-lined sheet, I brush each one generously with the beaten egg. This is what gives the dough that shiny, golden look once baked. I finish with a sprinkle of grated Parmesan cheese over the top of each one.
I bake these at 375°F for about 22 to 25 minutes, until the crust turns deep golden brown and the filling is bubbling through any small gaps. I always check with an instant-read thermometer to make sure the center hits 165°F. Letting them rest for five minutes before slicing keeps the cheese from spilling out everywhere.