Preheat your oven to 450°F and line a large rimmed baking sheet with parchment paper. Unroll the pizza crust on a clean surface and slice into 4 equal rectangles, each measuring about 5 1/2 by 3 1/2 inches.
Lay out each rectangle and gently spread 1 tablespoon of Caesar dressing evenly on each, making sure to leave a 1/2-inch border along all edges.
In the center of each rectangle, layer 1/2 cup of chicken leaving a 1-inch border on all sides. Season each rectangle with 1/4 teaspoon of salt and pepper. Sprinkle each rectangle with 2 tablespoons of crumbled bacon. Drizzle 1 tablespoon of Caesar dressing over the bacon. Top each rectangle evenly with 2 tablespoons of provolone and 3 tablespoons of mozzarella.
Carefully fold the dough over the filling to cover completely. Fold the short sides in like a burrito and roll up tightly to form a log. Seal the edges by pressing and crimping.
Lay the logs seam-side down on the baking sheet and generously brush all the logs with the remaining 1/4 cup of Caesar dressing, making sure to cover the tops and sides evenly.
Bake for about 10 minutes until the tops are starting to turn golden brown. Sprinkle each with the remaining 2 tablespoons of mozzarella evenly.
Place the rolls back in the oven until the cheese is gooey and golden, about 6 to 8 minutes. Let them cool for 5 minutes before serving.