Preheat the oven: Set it to 500°F (260°C) with a pizza stone or steel inside. Heat for at least 30 minutes so the surface is blazing hot. If using a sheet pan, preheat to 475°F (245°C).
Prep the dough: Dust your counter and hands with flour.
Gently press and stretch the dough into a 12–14 inch round. Avoid rolling pins if you want those airy edges.
Season the chicken: Toss the cooked chicken with a spoonful of pesto, a pinch of salt, and black pepper. This keeps it moist and flavorful.
Assemble the base: Transfer the dough to a floured peel or an oiled sheet of parchment.
Spread the pesto in a thin, even layer, leaving a 1/2-inch border.
Add cheese: Sprinkle shredded mozzarella evenly. Add torn fresh mozzarella, if using. Dust with Parmesan for a savory finish.
Top it off: Scatter the seasoned chicken over the cheese.
Add cherry tomatoes and a few onion slices. Finish with a light drizzle of olive oil and a pinch of red pepper flakes if you like heat.
Bake: Slide the pizza onto the hot stone/steel or place the sheet pan in the oven. Bake 9–12 minutes, until the crust is golden and the cheese is bubbling with browned spots.
Finish and serve: Let the pizza rest 2 minutes.
Toss arugula with a squeeze of lemon, a drizzle of olive oil, and a pinch of salt, then scatter on top. Slice and serve warm.