Dough: In a bowl mix muffin mix, salt, butter, shortening, 1 egg, vinegar, and water. Knead dough, and cut into 2 pieces. With a rolling pin, roll out each crust large enough to cover a pie pan. Place 1 crust in a pie pan and remove excess crust. Refrigerate until ready to use. Set aside remaining crust in the refrigerator.
Filling: In a bowl mix lime juice, tequila, Greek seasoning, and chicken breasts. Let marinate in refrigerator for 2 hours.
Preheat a grill or grill pan. Grill chicken until cooked through and juices run clear. Let cool and shred.
Preheat the oven to 375 degrees F.
In a medium saucepan, melt butter over medium heat. Add onions and cook until onions are soft, about 5 minutes. Add garlic and let cook for 1 minute. Remove heat; add 2 cans of cream of chicken soup, tomatoes, garlic salt, and green chiles. Stir in 1/2 cup of milk and 1 1/2 cups of cheese. Cook over medium heat for 10 minutes. Add shredded chicken and remove from the heat.
Pour filling into pie crust, add remaining 1 cup of cheeses, and cover with the reserved top crust. Cut small slits in top crust and flute edges. Mix 1/4 cup of water with remaining 1 egg and beat well. Brush the egg mixture over the top crust.
Bake for 30 minutes or until golden brown. Let cool 5 minutes.