Saute onion in butter until translucent. Add celery, carrots, garlic and broccoli and cook until tender (about 10 minutes).
Add flour and mix well. Cook stirring constantly for 2 minutes.
Gradually add chicken broth and evaporated milk stirring until well blended. Cook over medium heat stirring constantly until thick and bubbly. Stir in peas and corn, poultry seasoning, thyme, salt and pepper, and heat through.
Divide into 2 thawed, uncooked pie shells. Cover with the other shells and pinch edges to seal.
You can freeze one at this point.
Before baking, poke holes through the top with a fork for the steam.
Bake at 400 for 1 hour or until crust is golden and filling is bubbly. If frozen, reduce heat to 350, bake for 1 hour and turn up to 400 for 15 more minutes to brown crust. (Your oven may vary in temperature so keep an eye on it after the hour.).