Combine sugars and water in a heavy, medium-sized pan.
Turn heat on medium and bring to a boil, stirring every 2-3 minutes.
Boil for 1-2 minutes.
Remove from heat and add heavy cream and spiced rum.
Stir in vanilla.
Whisk in corn starch.
Cool and add to ice cream (recipe above) . Add only the amount desired and freeze for at least an hour before serving. Use the remaining butter rum sauce as a topping, heated.