Bring 2 quarts of water and 1/2 teaspoon salt to boil in a Dutch oven.
Add chicken and simmer for 8 to 10 minutes.
Remove chicken and add chicken bouillon to water. Turn heat up some and boil until reduced in half, about 10 minutes.
Let chicken cool slightly and then dice into bite-sized pieces.
In a large skillet, heat oil and butter over medium heat. Add onion and celery and sauté 2 minutes.
Add flour to skillet and whisk into oil/butter mixture to form a roux. Add Italian seasoning and pepper and cook 3 minutes.
Gradually whisk roux into water/bouillon mixture in the Dutch oven and bring to a boil.
Add potatoes and simmer 10 minutes.
Add vegetables and diced chicken and simmer 5-8 minutes
Stir in cream and simmer 3 minutes. Do a taste test and add additional salt to taste.
Preheat oven to 400 degrees. Unroll pie crust and place flat on a baking sheet. Bake until golden brown. Cut into pie shaped pieces and serve with soup.