Preheat the over to 425 degrees. In large mixing bowl, combine eggs, broth, milk, & flour. Season with salt & pepper. Stir to combine. Add in the potatoes, carrots, peas, green beans, chicken, & onion. Toss to combine.
Pour mixture into pie dish & cover with pie crust. Cut 5 slices (1 inch each) in center of pie.
Bake for 30-35 minutes until crust is golden brown & inside is bubbling through slices. (If pie crust begins to burn cover with foil & continue baking as instructed.)