Preheat the oven to 350 degrees F (175 degrees C). Line the bottom of an ungreased 9x13-inch baking dish with one can of crescent roll dough, pinching the seams together.

Melt butter in a saucepan over medium heat. Add chicken breast, rotisserie chicken, frozen vegetables, and sliced potatoes. Cook, stirring frequently, until vegetables are thawed and mixture is heated through, 5 to 7 minutes.

Meanwhile, warm both cans of condensed soup in a separate pan over medium-low heat. Slowly pour in milk and cook, stirring frequently, until combined and heated through, about 3 minutes.

Add soup mixture to chicken mixture; stir until well combined. Season with salt and pepper. Pour mixture into the prepared baking dish. Top with the second can of crescent roll dough; do not pinch the seams on these. Cover lightly with aluminum foil to prevent crescent rolls from browning too quickly.

Bake in the preheated oven until heated through and rolls are golden brown, 40 to 50 minutes.