In a small bowl, beat the egg and water together to create an egg wash
On a parchment-lined baking sheet, unroll pie pastry and cut crust to about ½ “ larger than a personal-size ramekin (12-ounce size)
Fold over and crimp the ½” extra crust, cut a few vent holes, lightly brush with egg wash, and parbake until light golden brown and no longer raw looking, about 7-10 minutes and then set-aside
In a medium saucepan over medium heat melt the butter. Add vegetables (except peas) and salt and sauté until vegetables are soft and slightly browned, about 9 minutes
Stir in garlic, thyme, and parsley and cook until fragrant then stir in flour and cook for about 1 minute
Slowly mix in cream, broth, and soy sauce,scraping the bottom of the pan to loosen any browned bits
Add chicken to the mixture and bring to a simmer. Cover and cook on low heat for about 10-15 minutes, stirring occasionally The internal temperature of the chicken should be 160℉
Transfer the chicken to a plate and shred with two forks
While the chicken is resting increase heat to medium and simmer for about 5 minutes until sauce is thickened and reduced to about 2 cups
Remove from heat and add cooked and shredded chicken (with any juices) and peas to the pan. Add salt and pepper to taste
Divide between ramekins and place crusts on top. Place on a baking sheet and bake until a bubbling and a deep golden brown, about 12 minutes.
Let pies rest 10 minutes before serving
Notes
If you don't have personal-size ramekins, use the same method in any 1qt baking dish. The baking times should remain the same.This dish can easily be doubled or tripled etc. for larger servings.If using canned mushrooms, wait to add them when you add the peas.