In a medium skillet, pour oil to a depth of 1/2-inch; heat oil over medium heat. Add tortillas, 1 at a time, and fry, about 1 minute per side until golden. (Press tortilla down with a fork if it starts to puff up while frying.) Drain on paper towels.
In a small bowl, combine sugar and cinnamon. Sprinkle evenly over hot tortillas. Set aside to cool. (Can be done 1 day ahead.)
Top cinnamon-sugar tortilla with 1 generous scoop of Homemade Cinnamon Ice Cream. Drizzle with chocolate syrup, and top with a cherry. Repeat procedure with remaining tortillas, ice cream, chocolate, and cherries.
In a 2-quart saucepan, combine half-and-half and cinnamon sticks. Cook 20 minutes over low heat (do not boil). Remove from heat. Remove cinnamon sticks and chill for 4 hours.
With an electric mixer at high speed, beat whipping cream until soft peaks form. Add condensed milk and continue to beat until stiff peaks form. Add chilled half-and-half.
Pour mixture into canister of a 4 to 6-quart ice cream freezer. Add milk, if needed, to fill canister to the freezer line. Freeze according to manufacturer's directions.