In a large bowl, mix flour, salt and baking powder; cut in shortening until crumbly. Gradually add water, tossing with a fork until dough forms a ball. Cover and refrigerate for 30 minutes.
Preheat oven to 375°. In another large bowl, combine beef, onion, potatoes, turnips, salt and pepper. Divide dough into 4 equal portions. On a lightly floured surface, roll one portion into a 9-in. circle. Mound 1.5 cups filling on half of circle; dot with 1 tablespoon butter. Moisten edges with water; fold dough over filling and press edges with a fork to seal.
Place on a parchment-lined rimmed baking sheet. Repeat with remaining dough, filling and butter. Cut slits in tops of pasties. Bake 30 minutes. If desired, pour milk into slits. Bake until golden brown, 20-30 minutes longer. Serve with ketchup.
Freeze option: Freeze cooled pasties in a freezer container. To use, reheat pasties on a parchment-lined baking sheet in a preheated 375° oven until heated through.