Add the jalapeño rounds, cucumber slices, and lime juice into a cocktail shaker and muddle gently to release the juices. Squash them together, until the cucumber is mostly broken down.
Add the tequila, Cointreau or triple sec, and simple syrup, in the cocktail shaker. Seal and shake vigorously.
Serve:
For salted rims, prep by rubbing a lime wedge along the rims. Dip in tequila salt or tajín for extra spice. Fill the glass with fresh ice.
Strain the cocktail into the prepared glasses and garnish with additional jalapeño rounds and a cucumber slice.
Notes
Make a pitcher by muddling 1 to 1 ½ jalapeños and half of a medium cucumber in slices with a little lime juice to help release the juices. Shake vigorously in a cocktail shaker. Strain the mixture into a pitcher and add 3 ½ cups silver or Blanco tequila, 1 ½ cups Cointreau or triple sec, ¾ cup lime juice (about 6 limes). Stir to combine and refrigerate until ready to serve over ice.