Add half the mint leaves to the simple syrup. Set aside to infuse, 10 to 30 minutes.
Add the tequila to a cocktail shaker filled halfway with ice. Add the simple syrup, lime juice and the remaining mint leaves. Cover and shake well.
Fill 2 to 4 glasses with ice. Squeeze a lime wedge into each glass and run it around the rim. Add the squeezed lime wedge to each glass and strain in the cocktail mixture. Add a mint sprig to each drink. Serve and enjoy!