Combine apple juice and cornstarch, stirring well. Pour apple juice mixture into a medium skillet. Bring to a boil, stirring constantly. Boil 1 minute. Remove from heat; add sugar, lemon juice, and cinnamon, stirring until sugar dissolves. Gently stir in blueberries.
Place brandy in a small saucepan, and heat just until warm. Pour brandy over blueberry mixture, and immediately ignite with a long match. Let flames die down.
Scoop 1/2 cup ice cream into each of 2 dessert bowls. Spoon blueberry mixture evenly over ice cream. Serve immediately.