Heat oven to 375°F. Line cookie sheet with nonstick foil or parchment paper.
Unroll pastry sheet on cutting board. In small bowl, stir together apple butter and cinnamon. Spread mixture evenly over pastry.
Starting with long side, roll up pastry jelly-roll fashion. With sharp knife, cut into 10 (1-inch) rolls; place rolls on cookie sheet.
Bake 18 to 22 minutes or until golden brown. Remove from oven.
In 1-quart saucepan, heat cider to boiling over medium heat. Boil, swirling occasionally, until reduced to 1/3 cup. Remove from heat; stir in cornstarch. Return saucepan to heat; boil 2 to 3 minutes, stirring frequently, until syrupy. Drizzle over baked rolls. Serve immediately.