Preheat oven to 375°F. Grease a 9×13 baking dish with butter and set aside.
In a large skillet, over medium-high heat, melt the butter. Add the onions and celery and cook until soft, about 3 minutes. Stir in flour. Slowly stir in chicken broth and whisk to combine.
Add the milk and salt, pepper, garlic, and celery seed. Reduce heat and simmer over medium-low heat until thickened, about 5 minutes. Add the chicken and vegetables. Stir to mix throughout. Pour the mixture into the prepared baking dish.
Unroll dough into 2 long rectangles; press perforations to seal. Place rectangles over chicken mixture; pinch center edges to seal. Press the outside edges of the dough to the edges of the baking dish.
Bake for 25-30 minutes, until the top is golden brown. Remove from the oven and brush with melted butter. Sprinkle with parsley, if desired. Cool for at least 10 minutes before serving.