Place basil, jalapeño slice(s) and grapefruit wedge in a cocktail shaker, and gently muddle to release oils and flavors. Add lime juice, simple syrup, tequila, grapefruit juice and ice. Cap the shaker, and shake until well chilled. Strain into a tumbler filled with ice, then top off with soda water. Stir to combine. Garnish with a grapefruit wedge.
* Jalapeño is used here to add subtle spice, so don’t go overboard with the heat. Jalapeños can vary in spice level, so start with just 1 to 2 thin slices. If you really can’t taste the heat, muddle in an additional slice in the next drink.
** Simple syrup is made by warming up equal parts sugar and water, and stirring until the sugar is dissolved. Recently I’ve been making this in the microwave! But you can also easily prepare on the stovetop.