Preheat oven to 375 degrees F. Lightly grease a 2-quart square baking dish; set aside. In a small saucepan cook and stir apple juice, brown sugar, and butter over medium-low heat until butter melts and sugar dissolves.
In a medium bowl stir together the granulated sugar and the cinnamon. Add apple wedges; toss to coat evenly. Unroll dough and separate at perforations into 8 triangles. Place a coated apple wedge along the shortest side of each dough triangle. Roll up dough around apple wedges toward the point. Arrange roll-ups in prepared baking dish. Slowly drizzle apple juice mixture over roll-ups, coating evenly; sprinkle with coarse sugar.
Bake in the preheated oven for 25 to 30 minutes or until golden brown and apples are tender. Cool for 30 minutes. If desired, serve with ice cream.