Whisk together the water, sugar, and brown sugar in a saucepan over med-high heat and bring to a boil. Add the remaining ingredients, except for the rum, and turn down the heat. Simmer, whisking occasionally, for 30 minutes.
Remove the pan from the heat, add the rum, stir and allow the mixture to cool for about an hour.
Pour the liqueur into a sealable bottle or jar. Store the liqueur in a cool location for 2-3 days to allow all of the flavors to blend with the alcohol. Enjoy this liqueur in your favorite cocktail or with your favorite Fall dessert!
Notes
Some people decide to strain the liqueur before placing it in the bottle. I decided not to do this because there were beautiful and delicious vanilla beans and residual pieces from the ingredients. I wanted those in my liqueur and in my drinks so I did not strain. If you want a clearer liquid, strain through a fine-mesh strainer and/or a cheesecloth before bottling.
You can substitute 1 teaspoon vanilla bean paste for the vanilla bean