Cook chicken in 1/2 cup broth until cooked.About 5 minutes. Reserve broth. Cool chicken.
Combine 2-1/2 cup flour, 3/4 teaspoons salt, 1/4 lb. butter and shortening until mix resembles coarse meal.
Toss 7-8 tablespoons cold water a tablespoons at a time. When mix begins to clump press into a ball, wrap and refrigerate.
Cut carrots in half length wise then chop. Bring water to boil with carrots. Cook until tender(about 5 min.)drain. Slice mushrooms.
In a large pan, add remaining.butter. Saute mushrooms until tender. Add 1 teaspoons salt and 1/2 teaspoons thyme. Cook about 5 minute.
Stir in remaining 1/4 cup flour and cook 1 minute Gradually stir in reserved broth. Add remaining 1-1/4 cup broth and cream. Bring to a boil and cook 1 minute stirring constantly.Remove from heat, pour off 1-1/2 cup reserve. Chop green onions. Stir in remaining ingredients.
Heat oven to 425 deg. Beat egg with 1 tablespoons water. Divide dough into 12 pieces. Roll to fit 5" pans. Fill with chicken mixture. Roll remaining 6 balls into top pieces. Flute edges. Cut vents in top.
Brush with egg mixture. put pies on baking sheet and bake at 450 deg. for 35 minute.