Simmer potato, carrot and broth in skillet 15 minutes until tender. Add chicken; cook until no longer pink in center, 5 minutes. Remove chicken and vegetables with slotted spoon to large bowl. Strain broth through sieve. Stir peas into chicken mixture.
Whisk milk into flour in saucepan. Stir in Parmesan. Cook over medium heat, stirring, until thickened, 5 minutes. Slowly stir in 1 cup reserved broth. Cook until thickened, stirring, 3 minutes. Add to chicken.
Preheat oven to 450°F. Coat 13 x 9-inch baking dish with cooking spray. Pour chicken mixture into dish.
Sauté onion in butter in skillet for 5 minutes. Sift together flour, baking powder, baking soda and salt into bowl. Cut shortening into flour mixture until it resembles coarse meal. Make well in center; pour in onions and buttermilk; toss with fork until ball forms.
Press dough out onto lightly floured surface into 12 x 6-inch rectangle. Starting with short end, fold dough over in half. Press out into rectangle again. Give dough quarter turn. Repeat folding and turning 10 times. With lightly floured rolling pin, roll into 14 x 5-inch rectangle. Cut lengthwise into 1/ 2-inch-wide strips. Arrange strips in crisscross pattern over casserole; trim lengths to fit; tuck ends down into side of dish.
Bake in lower half of 450°F oven 35 minutes until lightly browned and bubbly. Let stand 10 minutes.