Make the popcorn-infused rum: In a large container, combine the popcorn with the rum and set aside for 1 hour. Strain through a fine-mesh strainer into a container with a tight-fitting lid. Stir in the clarified butter, cover and set aside at room temperature for 24 hours. Transfer the container to the freezer and freeze until the fat solidifies on the surface, about 4 hours. Strain through a fine-mesh strainer and store at room temperature until ready to use. Use within 2 weeks.
Make the cocktail: In an ice-filled Collins glass, combine the popcorn-infused rum and the Coca-Cola, stir and serve.