Preheat the oven to 425°F (220°C). Lightly grease a large baking sheet or line it with parchment paper.
Place the cooked chicken in a medium bowl. Add 1/4 cup buffalo wing sauce and toss until the chicken is evenly coated.
In a separate small bowl, combine the ranch dressing with the remaining 1/4 cup buffalo wing sauce.
Lightly flour a clean work surface. Roll the pizza dough into a long rectangle of relatively even thickness.
Spread the buffalo ranch mixture evenly over the dough, leaving a small border around the edges.
Distribute the buffalo chicken evenly over the sauce.
Sprinkle the mozzarella and cheddar over the chicken, spreading the cheese evenly from end to end.
Starting from one long side, carefully roll the dough into a log. Pinch the seam and both ends firmly closed to help prevent the filling from leaking during baking.
Transfer the Buffalo Chicken Garbage Bread to the prepared baking sheet with the seam facing down. Lightly brush the outside with olive oil.
Bake for about 30 minutes, or until the bread is deeply golden and the dough is fully baked through.
Remove from the oven and allow it to rest for 5–10 minutes. Slice into thick pieces and serve warm.