Combine honey and water in the glass and stir vigorously until the honey is fully dissolved.
Add fresh lime juice and stir to combine.
Coat the bottom and sides of the glass with the mixture by swirling.
Fill the glass with cracked ice.
Pour the Cuban aguardiente over the ice.
Stir energetically from bottom to top until well combined and chilled.
Garnish with a lime wedge.
Traditionally served in an unglazed clay cup called a jícara, which slightly chills and subtly earthens the drink - if you can source one, it transforms the experience. Cuban aguardiente is an unaged cane spirit rougher than white rum; a light white rum is the closest modern substitute.
My Bar Shelf reads your shelf and shows you every cocktail you can make from what you already own, including Canchanchara.