Place the peas and carrots, green beans, and celery into a saucepan; cover with 3 cups water and two teaspoons Better than bullion chicken, bring to a boil, and simmer over medium-low heat until the celery is tender, about 8 minutes. Reserve the liquid and set the vegetables aside.
Melt the butter in a saucepan over medium heat, and cook the onion until translucent, about 5 minutes. Stir in 2/3 cup of flour, salt, black pepper, celery leaves, onion powder, and Italian seasoning; slowly whisk in the 1 and 3/4 cup reserved liquid and milk until the mixture comes to a simmer and thickens. Remove from heat; stir the cooked vegetables and turkey meat into the filling until well combined.
Fit 2 pie crusts into the bottom of 2 9-inch pie dishes. Spoon half the filling into each pie crust, then top each pie with another crust. Pinch and roll the top and bottom crusts together at the edge of each pie to seal, and cut several small slits into the top of the pies with a sharp knife to release steam.
Place pie on a cookie sheet or pie ring to catch possible drips. Cover the outer edge with a ring of foil or a pie crust shield. Bake in the preheated oven until the crusts are golden brown and the filling is bubbly, 30 to 35 minutes. Cool for 10 minutes before serving.