Place the fresh mint leaves and sugar in a tall glass or cocktail shaker.
Squeeze the juice from the lime wedges into the glass, then drop the wedges in as well. Use a muddler or the back of a spoon to gently muddle the mint, sugar, and lime together until the mint releases its aroma and the sugar begins to dissolve.
Fill the glass with ice cubes, packing them in tightly.
Pour the club soda or sparkling water over the ice, filling the glass to the top. Stir gently to mix the ingredients.
Taste and adjust sweetness by adding more sugar if desired. Garnish with a lime slice or a sprig of mint if using.
Serve immediately with a straw or spoon. Enjoy your refreshing virgin mojito!