Add ingredients to shaker along with 6-7 ice cubes and shake well. Strain into a 10-ounce glass and add fresh ice. Garnish with a jalapeño slice or ring.
To make jalapeño-infused tequila, muddle ½ jalapeño in large glass and add about 1 cup of blanco tequila. Taste after 30 minutes. If you would like it spicier, leave it longer, tasting every 10 minutes or so. When it reaches the spice level you like, strain out the jalapeño and it is ready to use. Remember, the spiciness will be balanced in the cocktail by the simple syrup, so make the tequila a little spicier than you want the cocktail to be.