This one is not from the Cheesecake Factory, but it is apparently a Cuban recipe.
MOJITOS FROM THE SOURCE
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Mojito recipe
This version is for the drink Ernest Hemingway himself enjoyed at the mojito's place of birth: La Bodeguita del Medio in Havana, Cuba.
1 teaspoon powdered sugar
Juice from 1 lime (2 ounces)
4 mint leaves
1 sprig of mint
Havana Club white Rum (2 ounces)
2 ounces club soda
Place the mint leaves into a long mojito glass (often called a "collins" glass) and squeeze the juice from a cut lime over it. You'll want about two ounces of lime juice, so it may not require all of the juice from a single lime. Add the powdered sugar, then gently smash the mint into the lime juice and sugar with a muddler. Add ice (preferably crushed) then add the rum and stir, and top off with the club soda. Garnish with a mint sprig.
** Optional ** While the following isn't the authentic original Bodeguita del Medio Cuban recipe for a mojito, some people will take half of the juiced lime and cut into four wedges to add to the glass. Another variation is to add Angostura bitters to cut the mojito's sweetness, which is a popular version in Havana hotels although not the true Bodeguita recipe. Some Cubans also use guarapo in place of the powdered sugar, which is a sugar-cane syrup available in some supermarkets or online Latin grocery stores.