Make the oolong tea syrup: Bring 1/4 cup water to a boil in a small saucepan and add tea. Cover and steep 5 minutes. Strain into a cup and then pour in sugar. Stir until it dissolves. Let cool.
Fill two cocktail glasses with ice. Fill a cocktail shaker one-third full of ice, then add 6 to 8 leaves mint and, if available, 3 to 4 shiso leaves. Pour in 2 tbsp. cooled oolong syrup, litchi purée, lime juice, rum, and pineapple juice. Shake vigorously.
Strain into the glasses, tuck a few herb leaves into ice, and serve.
Note: Nutritional analysis is per cocktail.