Preheat the oven to 425 F.
In a saucepan (about the 2-quart size), combine chick'n, carrots, celery, and peas. Add water enough to cover and bring to a boil. Then turn it down to a simmer for 15 minutes, uncovered.
After 15 minutes, remove from heat and drain veggies with a strainer over a 2-cup or larger heatproof measuring cup to reserve the liquid. Set veggies aside. Add enough water to reserved veggie cooking liquid to measure to 1 3/4 cups. Add the 2 teaspoons broth base or 1 veggie bouillon cube and mix together. Set aside. (If using broth rather than base or bouillon, then use enough to measure to 1 3/4, omitting the water)
In the same saucepan. veggies were cooked in, cook onion in the butter over medium heat until soft and translucent.
Whisk in flour, salt, pepper, and celery seed. Cook for a couple of minutes, then slowly stir in broth and then the non-dairy milk
Turn heat to low-med and simmer until thickened, stirring frequently. (A few minutes should do)
Put one pie crust into a pie plate and then spoon veggies into the crust. Pour hot broth over vegetables in the pie crust. Top with remaining pie crust and then cut a few slits in the top crust for steam to escape.
Place on a baking sheet and bake for 30-35 minutes until golden and bubbly.