Muddle one mint sprig with the Simple Syrup and the lime juice in the bottom of a mixing glass. Add the rest of the ingredients and shake with ice. Strain over cracked ice into a highball glass, top with soda, and garnish with the remaining sprig of mint.
In Havana, Hemingway liked to have his Daiquiris at La Floridita and his Mojitos at La Bodeguita del Medio. Although La Bodeguita is credited with popularizing the Mojito, there's a lot of controversy about the drink's origin. Some believe Constante Ribailagua of the Floridita made the first Mojito. The Mint Julep made in the southern United States beginning in the late eighteenth century from brandy, peach brandy, and eventually from bourbon was one of the first American cocktails to get international recognition, and some believe it sparked the creation of the rum version called Mojito in Cuba. The Mojito was a farmer's drink, sort of the Budweiser of Cuba, with its origins sometime between 1850, when the rum industry in Cuba modernized, in 1920. Those years brought important elements of the drink to Cuba for the first time, like ice and charged water. (The first shipments of ice arrived from New England in the 1850s, but you can bet only the wealthy had access until the turn of the century, when the first artificial ice plants began operation in Cuba.) A spicy sauce of the same name is used in the islands to marinate meat, but it seems to be unrelated to the drink.