Combine the half and half and cream in a medium saucepan and put on medium-low heat. Raise temperature to 175 degrees Fahrenheit or bring to a bare simmer if a thermometer is not available.
Once at temperature remove from heat and add rosemary, nutmeg, sugar, and chocolate syrup and whisk to combine.
Let mixture cool to room temperature.
Once Cool, combine the brandy with the mixture and immediately move to a closed container and place in the bottom of your fridge. Allow the flavors to mellow until the mixture is thoroughly chilled, preferably overnight.
Once chilled and aged properly, add mixture to your ice cream maker (strain if you don't want the rosemary or nutmeg bits) and churn in accordance with the manufacturer's instructions (most churns will finish within 25-30 minutes).
Mixture will be slightly less than soft-set due to the alcohol when finished churning. Quickly transfer to a closed container and allow it to harden in the freezer overnight. The finished ice cream will continue to harden over the next few days, but can be served as refrigerator soft-serve after an overnight chill.
Serve in chilled martini glasses (to help prevent hand-heat from melting the ice cream) and garnish with mint, chocolate shavings, or a dusting of cocoa mix.