Since Kahlua is a trademarked product, the closest act of homage would be to aim for a smooth coffee liqueur that matches the original's blend of ingredients native to Veracruz, Mexico: namely coffee, rum and sugar. The liqueur itself is easy to make, with plenty of scope to experiment with supporting flavors.
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The coffee is arguably the most distinctive ingredient of a Kahlua-inspired liqueur, but you can still make a perfectly good liqueur without an encyclopedic knowledge of bean varieties. The original Kahlua uses Veracruz estate-grown, roasted and ground arabica beans only, but plenty of home mixers report success with plain instant coffee or ground arabica brewed in large quantities. If using ground coffee, you will need to filter the end product to remove any remaining fine grit. In all cases, brew the coffee for at least an hour for an intense, rich flavor. The copious amounts of sugar to be added will temper the bitterness.
Sweeten the Mix
Kahlua calls for a formidable dose of sugar, with the original using a combination of brown and white sugar. Add a cup of sugar for each cup of water in the coffee brew, and leave to simmer for another hour, stirring frequently until the coffee is syrupy. If using instant coffee, however, you can mix everything together from the start as there is no brewing to take place. Once the coffee and sugar are thick and velvety, remove from the heat and allow the mixture to cool.
Choose a Spirit
Authentic Veracruz Kahlua uses rum to complete the sublime trinity of regional ingredients, with an end product that contains only 20 percent alcohol. You can also use vodka or brandy as the base spirit; think of those choices as a kind of shortcut to a Black Russian or Dirty Mother cocktail, respectively. In all cases, you can get away with using a mid-range bottle of standard spirit rather than a superior blend, since the strong coffee and sugar flavors will overpower any subtleties in the spirit's flavor.
Define the Flavors
Background flavors provide more of a reason to savor homemade Kahlua. The original uses cinnamon, hazelnut and peppermint during the mellowing process, but split vanilla beans or a dash of vanilla extract will also render a pleasant aroma. Once the liqueur mixture has cooled, add the flavorings and transfer to a sterilized bottle and leave for at least a couple of weeks in the dark, stirring occasionally to agitate any sediment. Taste it frequently and once you have the required blend, strain to remove the vanilla beans and any sediment and enjoy.