Cook chicken breasts (I put them in the crock pot with the chicken broth and cooked them on high for about 3 hours until they shredded easily with a fork). Strain and reserve the broth.
Meanwhile, melt 1 Tbl. butter in a Dutch oven. Saute onion, carrot, and celery with herbs until tender. Season with poultry seasoning, salt & pepper. Remove from Dutch oven and reserve.
Preheat oven to 450 degrees.
Add remaining 4 Tbl. butter to the pot. Once melted, dust with flour; stirring constantly for 1-2 minutes. Pour in reserved broth and bring to a boil, whisking until thickened. Add in shredded chicken, corn, peas and reserved sautéed veggies. Mixture should be thick. Adjust seasoning to taste.
Place one pie crust in 9-inch pie plate. Pour in filling. Top with second pie crust and crimp and trim edges. Use trimmed crust to make decorative shapes for top. Cut slits in top crust to vent. Brush crust with beaten egg. Place pie on baking sheet and bake on center rack for 30 minutes. Check crust after 10 minutes and cover edges with foil if beginning to brown.
Allow to cool for 10 minutes before serving.