Mix the creme de menthe, creme de cacao, irish cream, vodka, and half-and-half in a pitcher and freeze for 1 hour.
Chill 6 martini glasses in the freezer for 30 minutes.
For each drink, shake a little more than 5 ounces of the mixture in a shaker with ice and strain into the chilled glasses or serve over ice in short glasses.
Garnish with chocolate shavings, if desired.
Make-ahead: this can be made up to 8 hours ahead and kept in the refrigerator.