Turkey pot pie with a crispy Parmesan crust

Name: Turkey pot pie with a crispy Parmesan crust
Ingredients: 2 tablespoons canola oil; 1/2 cup celery, diced; 1/2 cup carrots, diced; 1/2 cup onion, diced; 1/2 cup parsnips, peeled and diced; 1 cup button mushrooms, sliced; 1/4 cup flour; 2 1/2 cups Turkey or chicken stock (homemade is best, but whatever you have is great); 2 teaspoons poultry seasoning or powdered turkey gravy mix; 2 cups turkey, cooked and shredded; 1 cup frozen peas, thawed; 1 cup frozen green beans, thawed; 1/4 cup half and half; Salt and pepper to taste; 6 sheets of phyllo dough; 1/4 cup Parmesan cheese, finely grated