Combine brown sugar, cornstarch, cinnamon, and salt in a medium pan. Add the half and half, and stir over medium heat until the mixture thickens. Remove from heat, and allow the mixture to cool. Stir in the applesauce, lemon juice, and vanilla. Cover and refrigerate until cold or overnight.
Stir the cold apple mixture well, then freeze in your ice cream machine according to manufacturer’s instructions. When finished, the ice cream will be soft, like soft serve. For firmer ice cream, freezer at least 2 hours.
To serve, scoop ice cream and top with crushed graham crackers, a sprinkle of cinnamon, and a bit of whipped cream.