Add 2 tablespoons of the butter to a skillet and melt over medium-high heat. Add the apples and saute for 5 minutes. Remove to a plate and set aside.
In the same skillet over medium heat, add the brown sugar and the remaining stick of butter. Stir it around until the butter melts and the sugar dissolves, then pour in the cream. Stir it around and let it bubble up and thicken for about a minute. Turn the heat to low and add the apples back to the skillet. Sprinkle in the cinnamon, stir the mixture and let it thicken for another 1 to 2 minutes.
Spoon big scoops of vanilla ice cream into sundae glasses and drizzle over the caramel apple sauce.