Melt the butter in a large skillet over medium heat. Add the onion, celery, and cubed potato. Cook for about 5 to 7 minutes, stirring occasionally, until the onion and celery have softened and the potato has started to become tender.
Add the salt, black pepper, celery seed, rosemary, poultry seasoning, garlic powder, and bouillon. Stir well to combine.
Sprinkle the flour over the vegetables and stir until well incorporated. Cook for about 1 minute, stirring frequently.
Slowly stir in the milk and cook over medium-low heat until the mixture begins to thicken. Then gradually stir in the chicken broth.
Bring the mixture to a gentle simmer over medium-low heat. Cook, stirring frequently, until the sauce has thickened and the potato is tender.
Stir in the cooked chicken and frozen mixed vegetables. Cook for another 2 to 3 minutes, stirring occasionally.
Taste the filling and adjust the seasoning with additional salt, pepper, bouillon, or garlic powder, if needed.
The filling should be thick and creamy but still easy to spoon. If it is too thick, stir in a small amount of chicken broth or milk.
Remove the skillet from the heat and let the filling cool for about 10 to 15 minutes while you prepare the crust.