Place the mint leaves and sugar in a sturdy pitcher. Use a muddler to press the leaves gently until the sugar dissolves and the mint releases its aroma.
Pour the lime juice into the pitcher and stir to combine the mixture evenly.
Add the crushed ice to the pitcher, then slowly pour in the club soda.
Stir once or twice to blend the ingredients without losing too many bubbles.
Divide the drink among four glasses, making sure each one gets a good amount of ice and mint.
Add one mint sprig and one lime wedge to each glass before serving.