Prepare dough first. In a medium sized mixing bowl, combine flour and margarine; with a pastry blender or the back of a fork, cut in margarine until mixture resembles coarse meal. Add in yogurt and mix thoroughly.
Form dough into 4 equal balls. Cover each portion with plastic wrap and refrigerate for 30 to 40 minutes (can be kept in refrigerator for up to 3 days, or frozen in freezer until ready to use). If dough is frozen, make sure to thaw completely before using.
For the filling: in a large stockpot, dissolve the flour in the broth with a whisk, and bring the broth mixture to a boil. Add carrots, mushrooms, and onions. Reduce heat to medium-low, cover, and cook until carrots are tender (about 10 minutes).
Add remaining ingredients except dough (cooked chicken, frozen peas; salt and pepper to taste). Cook uncovered, stirring occasionally, for 5 minutes. Divide mixture evenly among 4 individual casseroles (or 16 oz. soufflé dishes).
Roll 1 ball of dough between 2 sheets of wax paper, forming a circle slightly larger than the top of the casserole. Lift dough onto 1 filled dish. Using a fork, press edges of dough to rim of dish; gently pierce top of dough to allow steam to escape. Repeat procedure for other pies. Pies can now be wrapped and frozen for future use, or placed into a pre-heated 375 degree oven.
Place pies on a baking sheet and bake at 375 for 30-35 minutes, or until crust is lightly browned (will be 40-45 minutes if pies are frozen).
Let pies cool for 10 minutes before serving.