Pour Coke into a 9" x 13" glass baking dish. Add rum and gently mix to combine. Add lime lest and mix again.

Transfer dish to freeze and place on a flat surface. Freeze for 1 hour. Using fork tines, rake and break up granita; spread out granita in dish. Freeze for 30 minutes, and then rake granita again; spread out in dish.

Repeat until granita is completely frozen and flaky. Spoon into a martini glass and serve with a lime wedge to garnish.