Creamy vegan mocha granita

Lester got me an ice cream maker for my birthday (hooray!). And of course, knowing nothing about ice cream, what do I do--make up something completely off-recipe for my second-ever attempt. I had all the things, and wanted something that I wouldn't feel bad having with breakfast.

1.5 c cold coffee
1 c rice milk
3/8 c sugar
1/4 c vegan coconut-milk chocolate ice cream (I know, ice cream in ice cream, crazy)
10 drops John's coffee bitters

Whisk together all the ingredients, preferably wearing the cute dress I just got for Cait&Jay's wedding, and put the mix in the ice cream maker. After 10 minutes there was some residual liquid but the frozen part wasn't being stirred, so I stopped it then. Scoop into 3-6 serving glasses and serve immediately. Or as I did, scoop into 3 jam jars and put in the freezer overnight, and remove from the freezer 20 minutes before serving. Serving suggestions: with brioche.