Stir tequila, lime juice, orange liqueur, and simple syrup together in a pitcher with a lid; add jalapeno pepper and thin cucumber slices. Refrigerate at least 1 hour.
Run a wedge of lime along the rim of each of four pint glasses.
Spread kosher salt onto a flat plate; press glass rims into salt to coat. Fill glass with ice and pour margarita over the ice.
