I'm not going to try and claim this is anything close to a traditional Mai Tai because I don't dare face the wrath of Mai Tai aficionados. Think of this as a Mai Tai light as it's tamed with passion fruit juice (look for the 100% juice kind, not the sugary soda-like stuff in most stores), but it is thoroughly Mai Tai in every other respect.
(no added sugar)
Smack a few leaves of mint and drop into a cocktail shaker. Combine passion fruit juice, light rum, lime, orange liqueur, and simple syrup in a cocktail shaker and fill halfway with ice. Shake about 10 to 15 seconds then strain into a chilled rocks glass, add a few cubes of ice, and garnish with remaining mint leaves.
To float the aged rum (see photo below), place the tip of a spoon perpendicular to the inside edge of the glass, turn the curve of the spoon toward the ceiling, and slightly angle the spoon downward. Slowly pour the liquid to be floated down the spoon toward the inside of the glass and, so long as the liquid is less dense than the other liquids in the glass, it will float.
Traditionally, a Mai Tai is made with an orange flower and almond syrup called orgeat. Because it is hard to find, I call for standard simple syrup. Use a traditional rich simple syrup (aka 2 parts sugar to 1 part water) and, if you'd like spice it further with spices such as ginger, allspice, cloves, cinnamon, or orange zest.