With the rack in the lowest position, preheat the oven to 190 °C (375 °F).
In a saucepan off the heat, combine the sugar and cornstarch. Add the applesauce and bring to a boil, stirring constantly. Stir in the apples and vanilla. Set aside.
In a bowl, combine the dry ingredients. Add the butter and stir until the mixture is just moistened.
Line a 23-cm (9-inch) pie plate with the pie crust. Remove any excess dough. Fill with the apple mixture. Sprinkle with the crumble. Bake for about 40 minutes or until the crumble is golden brown. Cool on a wire rack. Serve warm or cold.