Miss Debbie and I invented this the other night. It was delicious! You'll need an ice cream maker for this. Be careful with the alcohol--too much and this won't freeze.
The day before put your ice cream maker container in the freezer (I store mine in the freezer so that it's always cold.) and make your simple syrup.
Juice of 6 lemons or 9 limes or a combination
2 cups simple syrup, cooled (2 cup of water boiled w/ 2 cups of sugar & the mint)
Big handful of fresh mint leaves
grated rind of lemons &/or limes
grated rind of 1 orange
2 shots of white rum
1 shot Cointreau or Grand Marnier
Make the simple syrup by boiling 2 cups of water w/ 2 cups of sugar until the sugar is dissolved. Add the mint. Let cool and strain. You can make this ahead and keep in the fridge. You can use this to make regular mojitos too.
Mix 2 cups of simple syrup with all other ingredients. Taste and add more lemon/lime juice if necessary. This should be highly flavored because the cold tends to make things taste blander.
Pour into ice cream maker and freeze according to directions.
You could probably make this into a granita as well, by freezing it in a shallow baking pan and scraping it up after a few hours of freezing, refreezing, and scraping again.