Assemble all ingredients, including pie crusts.
Melt butter in 12” skillet.
Add onion, carrots, celery, and salt to the skillet. Cover and cook 6 minutes on medium until veggies are soft, not browned.
Remove from heat and add flour a Tablespoon at a time, and mix until veggies are thoroughly coated.
Return to heat and stir in chicken broth, then half & half, and bring to boil on medium high heat – about 3-4minutes, stirring constantly.
Mix in diced potatoes, pepper, and thyme, cover and turn down heat to medium low.
Simmer until potatoes are tender,about 8-10 minutes, stirring often. Remove from heat.
Add chicken and mix thoroughly, then add drained peas and stir again.
Preheat oven to 450.
Place one crust in deep 9” pie pan.
Place all the chicken mixture into the pie pan, then cover with the second crust.
Crimp the edges of the top and bottom crusts together to seal in the mixture.
Brush the top with an egg yolk wash.
Prick the top crust with a fork several times to allow steam to release.
Place pie on sided aluminum cookie tray and set on rack in bottom third of the oven.
Bake at 450 for 18 minutes, then rotate cookie tray. Lower heat to 375.
Bake at 375 for an additional 15 minutes, until crust is golden brown.
Note: if crust edges are browning too quickly, cover the edges with pie shields, or strips of aluminum foil.
Remove from oven and let stand for 10 minutes, for easier slicing. Serve while still warm.