Preheat the oven to 425 degrees F (220 degrees C). Place 1 pie crust in a 9-inch pie plate. Set aside second crust.

Remove skin from rotisserie chicken and shred meat.

Melt butter in a large saucepan over medium heat. Add onion and cook until tender, about 5 minutes. Add flour, salt, and pepper; stir until a paste is formed, 2 to 3 minutes. Add broth and milk, stirring until thickened, about 5 minutes.

Add chicken and vegetables, stirring until combined. Pour mixture into the prepared pie plate. Place second crust on top, sealing edges and making several slashes on top. Wrap edges with foil to prevent them from browning too fast.

Bake in the preheated oven until top is golden brown, 25 to 30 minutes.