In a bowl, combine chicken, lemon juice, and soy sauce. Marinate for about 10 to 15 minutes. Drain meat, reserving liquid.
In a wide pan over medium heat, heat oil. Add chorizo de bilbao and cook for about 1 to 2 minutes or until lightly browned.
Add chicken and cook for about 3 to 5 minutes or until lightly browned. Remove from pan and set aside.
Wide down pan as needed. Add butter. When it begins to melt, add onions and garlic and cook until limp.
Add flour and cook, stirring regularly, until lightly browned, bubbly and begins to smell "nutty'.
Add water and reserved marinade,, whisking vigorously to prevent lumps. Bring to a boil until smooth and slightly thickened.
Return chicken and chorizo to pan. Season with salt and pepper to taste. Lower heat, cover and cook for about 15 to 20 minutes or until chicken is cooked through.
Add carrots and cook for about 3 to 5 minutes or until tender.
Add green peas, mushrooms, Vienna sausage, and evaporated milk. Stir to disperse. Continue to cook for about 3 to 5 minutes or until vegetables are heated through and sauce is thickened.
Transfer filling onto an oven-safe baking dish. Gently top filling with the crust and seal edges with a fork, trimming edges if necessary. Cut about a 1-inch vent on the crust.
In a bowl, combine egg wash: egg and water. Whisk together until well blended. Lightly brush top of crust.
Bake pie in a 400 F oven for about 20 to 30 minutes or until filling is bubbly and crust is golden. If needed, cover edge of crust with strips of foil at the last 5 to 10 minutes to prevent from excessive browning. Remove from heat. Allow to stand for about 5 minutes and cut into serving portions.