Preheat oven to 450 degrees F (230 degrees C). Butter a 2-quart casserole dish.
In a large saucepan, saute chopped onion in the butter. Stir in flour and cook for 1 minute. Add chicken broth and milk. Heat to boiling, stirring constantly. Reduce heat to medium and cook and stir for 2 minutes more. Season with salt and pepper. Add frozen peas and carrots and cooked chicken. Pour into prepared casserole dish.
In a medium bowl, mix together 2 cups flour, baking powder, and 3/4 teaspoon salt. Cut in shortening until mixture is crumbly. Stir in milk just until dough is moistened, then drop by spoonfuls onto chicken mixture.
Bake at 450 degrees F (230 degrees C) for 12 to 15 minutes, or until biscuits are golden brown, and cooked on the bottom. This tends to bubble over so I place a piece of aluminum foil under the pan to catch the drips.