Preheat oven to 375 degrees
In a non-stick skillet, cook the chicken over medium heat until cooked through. Set aside and dice once cooled.
In the same pan you used to cook the chicken, add the broccoli and peas and sauté for 1 minute, then add 1 teaspoon of soy sauce and cook for another minute. Add in the diced chicken and an additional teaspoon of soy sauce and mix together well. Place in a bowl and set aside.
Return the empty pan back to the heat and add butter, cook over medium heat until melted, then add minced garlic and cook until fragrant. Whisk in the flour, then slowly stir in chicken stock and another teaspoon of soy sauce and stir sauce until thickened. Pour the sauce over the vegetables and chicken filling and stir to combine.
Pour the contents into 6 ramekins and place the ramekins on a foil lined baking sheet.
On a floured surface, roll out pie crust to ⅛ inch thick and use cookie cutter to cut out 6 circles. Place each circle on top of each ramekin and press sides against ramekin dish to seal.
Crack an egg into a small dish and add water. Beat the egg and water mixture with a fork and then brush top of each pie crust with egg wash.
Cut a small slit into the top of each pie crust and place in oven for 15 minutes or until crust is golden brown.