Boil 1 cup of water with 1 cup of sugar until fully dissolved. Remove from the heat and stir in your lime zest with the 1/4 cup mint leaves. Cool to room temperature, strain, and refrigerate.
Assembling your drink:
When ready to serve, place 2 mint leaves into the bottom of a cocktail glass. Squeeze 1 lime wedge into your glass and muddle with the back of a spoon.
Stir in 2 tablespoons of your mint lime syrup.
Top with ice, 1 shot of tequila, and club soda. Stir and enjoy.