Preheat your oven to 400 degrees. This ensures your rolls bake evenly and become golden brown.
In a medium pan, heat a tablespoon of olive oil. Once hot, add the sliced onion and red bell pepper. Sauté them until they are crisp-tender, which takes about 5 minutes. Set them aside to cool slightly.
On a lightly floured surface, unroll the Pillsbury Classic Crust Pizza Dough. Gently roll it out with a rolling pin to flatten it slightly. This creates a better surface for your filling.
Spread the refrigerated pesto evenly over the dough, ensuring every corner is covered with that aromatic flavor.
Sprinkle the sautéed onion, red bell pepper, chopped cooked chicken, and both cheeses over the pesto. Make sure to distribute evenly for the best flavor in each bite.
Starting from a long edge, tightly roll the dough up jelly-roll style. This creates a nice, even log of filling.
Once rolled, slice the log into 12 equal pieces. Each slice should be about an inch thick, which allows them to bake evenly.
Place the sliced rolls cut side down in a lightly greased 12-inch cast iron pan or on a greased baking sheet. Be sure to leave some space between them as they will puff up while baking.
Bake in the preheated oven for about 18 to 20 minutes, or until the rolls are golden brown and the cheese is bubbly. Keep an eye on them to avoid burning.
Once done, remove from the oven and serve warm with marinara sauce on the side for dipping. Enjoy!