Heat a nonstick skillet over medium-high heat. In a medium bowl, combine the sugar, ginger and lime zest. Add the pineapple and toss.
Scrape the pineapple into the skillet, add the star anise and cook, without stirring, until the pineapple caramelizes, 5 minutes. Stir in the rum and let the alcohol burn off, about 3 minutes. Remove from the heat and stir in the orange juice, scraping the bottom of the pan; let cool.
Discard the anise. Puree the fruit mixture in a blender. Stir in the white wine and pour the mixture into ice-pop molds. Freeze until solid, about 4 hours.
