1. In a 2- to 3-quart pan, cover rice with 1 2/3 cups water. Bring to a boil over high heat; cover, reduce heat, and simmer 15 minutes. Remove from heat; let stand, covered, 15 minutes longer.
2. Meanwhile, mix 1 cup broth with oyster sauce, cornstarch, garlic, and chili flakes; set aside. Thinly slice steak across grain into 1/8-inch-thick slices. Add oil to a 10- to 12-inch nonstick frying pan over high heat; when hot, add meat. Cook, stirring constantly, until meat is no longer pink, about 4 minutes. Add remaining broth, stir-fry vegetable mixture, and onions. Cook, covered, just until vegetables are bright green, about 3 minutes. Stir seasoned broth into meat mixture; bring to a boil.
3. In a bowl, combine rice with meat-vegetable mixture; spoon into a 10-inch pie dish, 9-inch square pan, or 1 1/2-quart baking dish.
4. Unfold pie crust according to package directions. On a lightly floured board, roll into a 12-inch round for pie dish, or 1 inch larger than dish of another shape. Place over beef and vegetable mixture; fold edges under and flush with pan rim, and flute firmly against rim. Cut shapes from crust and decorate top, or make a couple of decorative slits in crust.
5. Bake in a 350° oven until filling is hot in center, about 1 hour. Lay foil over crust if it begins to overbrown. Let cool about 10 minutes; spoon from dish or cut into wedges.