Brew tea according to package label instructions. Let cool.
Place a shiso leaf and a lime slice on the bottom of a cocktail shaker. Using a muddler, press down on shiso and lime and twist gently a few times to release the flavors. (Don’t muddle very hard, or shiso can turn bitter.) When the mixture is fragrant, it’s ready.
Add 1½ ounces green tea, gin, and honey into shaker; shake or stir well until honey has dissolved. Add a splash of soda; gently stir. Place ice cubes in a rocks glass; strain cocktail over. Garnish with remaining shiso leaf and lime slice.