When ready, preheat the oven to 450°F.
In a medium bowl, stir together the ranch dressing, buffalo sauce, and shredded chicken.
Pour the remaining oil mixture into a 12-inch, cast-iron skillet. Use a pastry brush to coat the pan.
Add half the dough to the skillet and work the dough to the edges. Use your fingers to create dimples in the dough.
Top the dough with 1 cup of the chicken mixture, ½ cup of the cheddar cheese, and ½ cup of mozzarella.
Fold the other half of the dough out onto a sheet of parchment paper. Use your hands to form the dough into a 12-inch circle. Invert the parchment paper over the cheese and carefully peel back the paper, leaving the top layer of dough in the skillet.
Use your fingers to gently dimple the top of the dough. Top with the remaining chicken mixture and bake for 12 minutes.
After 12 minutes, top with the remaining cheeses and bake an additional 14-16 minutes, or until the cheese is melted.
When done, drizzle extra buffalo sauce and ranch dressing over the pizza. Serve hot, garnished with parsley (optional).