Lightly muddle (see Note) the mint in a cocktail shaker until fragrant and lightly smushed. Add the rum, lime juice, sugar, and about 1 cup of ice. Cover, and shake until the outside of the shaker is cold and beaded with moisture.
Fill two highball glasses with ice. Divide the mojito between the glasses. Top with the club soda, dividing it between the two glasses. Garnish each glass with more mint leaves and a slice of lime in each.
Notes
Muddlers are available in a variety of material, though the most popular is made of a soft, uncoated wood. They are about 6 inches long and have a flat end on one side. They are used for mashing fruit, sometimes with sugar, to release juice. To muddle, place the mint in the bottom of a cocktail shaker, or a sturdy glass. Use the flat end of the muddle to press the fruit, twisting as you go. You’re aiming to slightly crush and break down the herbs to release more flavor and aroma. Be gentle if you are muddling herbs on their own; it doesn’t take all that much to release the most flavor from delicate herbs.