This (made correctly) is the the classic mojito, Add 2 tea spoons of white sugar to a hi ball, add the lime juice, get 2 fresh thick steamed spigs of mint and snap them, add them to the glass and gently push them to the bottom of the glass, DO NOT muddle or crush them. add the rum and a little soda, stir then add CUBED ice, strier again and then top with more ice and soda.
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Here are our top picks from Amazon of cocktail making equipment to make a Mojito (traditional cuban style).