Preheat your oven to 425°F (220°C).
In a skillet, heat the olive oil over medium heat. Add the sliced onion and red bell pepper. Sauté for about 5-7 minutes or until the vegetables are tender and slightly caramelized. Remove from heat and set aside.
On a lightly floured surface, unroll the Pillsbury Classic Crust Pizza Dough. Use a rolling pin to spread it into a rectangle, about ¼ inch thick.
Spread the refrigerated pesto evenly over the dough, leaving a small border around the edges. Sprinkle the sautéed vegetables, chopped chicken, shredded mozzarella, and grated Parmesan cheese over the pesto layer.
Starting from one end, carefully roll the dough into a log shape. Pinch the seams to seal the roll.
Using a sharp knife, slice the rolled dough into 1-inch thick pieces. Place the rolls on a baking sheet lined with parchment paper.
Bake in the preheated oven for 15-20 minutes, or until the rolls are golden brown and the cheese is bubbling.
Once baked, remove the rolls from the oven and let them cool for a few minutes. Serve warm with marinara sauce on the side for dipping.