In a large pot, bring water to a boil, add the chopped potatoes and sliced carrots and boil until soft when poked with a fork (8-10 mins). Drain and set aside.
In a large skillet melt butter over medium heat. Add onion and sauté until soft. Stir in flour, thyme, salt and pepper and mix until combined. Gradually whisk in broth and milk, stirring to keep mixture smooth. Bring to a gentle boil and cook 2 minutes until thickened. Add cooked chicken, peas, corn, potatoes, and carrots and stir until everything is evenly distributed.
Line each pie plate with the bottom pie crust. Divide the filling between the two pies. Top with second crust and pinch the edges to seal the crust. You can also use a fork to press down on the edges and make lines going around the rim of the pie plate.
Bake at 425 degrees for 35-40 minutes until golden. I usually tear pieces of tin foil to cover the edges of the pie so they don't burn. Let stand 15 minutes before cutting and serving.