Cornbread Chicken Pot Pie

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1 (3 1/2 pound) chicken

5 cups water

1 onion

2 ribs celery, chopped

2 bay leaves

1 sprig fresh thyme

6 peppercorns

Sauce:

2 tablespoons unsalted butter

1/2 cup chopped onions

1/2 cup chopped celery

2 cup chicken stock or canned broth

1 cup milk

6 teaspoons all-purpose flour

1 (10-ounce) package frozen mixed vegetables, thawed and drained

1 tablespoon chopped fresh parsley

1 teaspoon salt

1/4 teaspoon ground black pepper

Cornbread:

1 1/4 cup yellow cornmeal

1 cup all-purpose flour

2 1/2 teaspoons baking powder

1 teaspoon sugar

1 teaspoon salt

1/4 teaspoon chili powder

1 cup milk

2 large eggs

1/4 cup vegetable oil or melted butter