Preheat oven to 400 degrees F. Butter a 9x13 casserole dish or baking pan.
In a large skillet heat 1 tablespoon oil over medium heat. Season the chicken well with salt, pepper and 1/2 teaspoon Italian seasoning. Add to skillet and cook through, stirring often. Remove to a large bowl and set aside.
Turn the heat down to medium-low and add the remaining 2 tablespoons oil, the onion, carrots, celery, garlic and 1/2 teaspoon Italian seasoning. Cook 7-8 minutes, stirring often, stir in the peas and cook 2 more minutes. Remove the mixture from the pan to the bowl with the chicken.
With heat on medium-low melt 3 tablespoons butter in the pan, whisk in the flour and cook 3 minutes. Slowly whisk in chicken broth then the milk. Turn heat up to medium-high and bring to a simmer for 3 more minutes, stirring often.
Add the chicken broth to the bowl with the chicken/vegetables and mix well, then mix in both cheeses.
Pour the mixture into the buttered casserole and spread out evenly.
Roll the pie crust out on a lightly floured surface to about 10-inches in diameter and cut circles out of it with a biscuit or cookie cutter. Arrange them over top of the pasta.
Bake 30 - 35 minutes until the casserole is hot in the center and the crust is golden brown, if the crust starts to darken too much cover with aluminum foil. Let set 5 minutes before serving.