In a large saucepan, add the diced potatoes, sliced carrots, and water to cover. Bring the water to a boil, then reduce and cook, covered, 8-10 minutes or until the veggies are crisp-tender. Drain out the water and set aside.
In a large skillet, heat the butter over medium-high heat until melted. Add the onion, and cook and stir until tender.
Add the flour to the butter and onion, and stir until blended. Add in the seasonings, the broth, and the milk and stir until blended. Bring the mixture to a boil, stirring constantly, and cook about 2 minutes or until nicely thickened.
Add the cooked chicken, peas, corn, potatoes, and carrots. Lower the heat to low and cook and stir until everything is well combined.
Pour the mixture into a large pie dish. Unroll a thawed puff pastry sheet and use to cover the top of the pie dish and mixture. If the puff pastry covers the entire plate, cut vents in the top.
Heat oven to 425F. Bake the chicken pot pie for 30-35 minutes or until the crust is lightly browned and cooked through.
Let the pie stand and cool about 15 minutes before serving. Then serve and enjoy!