Roll 1 sheet of puff pastry into 11-inch square, press into 9-inch pie dish, trim excess, and prick with fork. Cover with aluminum foil.
STEP 3
Bake until puffed and golden, about 25 minutes. Remove foil and set aside.
STEP 4
In a skillet, melt butter over medium-low heat. Cook chopped onions and celery until soft, about 5 minutes. Add flour, salt, pepper, and celery seed; stir until paste-like.
STEP 5
Slowly add milk while stirring. Gradually incorporate chicken broth until thickened, about 7 to 10 minutes. Stir in chicken and frozen vegetables; cook until vegetables are thawed, 3 to 5 minutes.
STEP 6
Pour chicken mixture into pre-baked pastry shell. Roll out second sheet of pastry, cover filling, trim excess, and crimp edges.