Combine brown sugar and regular sugar and divide.
Simmer the following over medium heat: cream, milk, 1/2 of sugar mixture, and nutmeg.
Whisk together eggs, remainder of sugar, 1/8 tsp salt. Add cream in a steady stream continuously whisking. Return to saucepan and stir with wooden spoon and register 125 degrees, do not boil.
Strain custard through sieve in metal bowl. Stir in liquors and mint syrup. Chill for 6 hours. Freeze in ice cream maker and transfer to an airtight container. Freeze.
Combine in saucepan. Bring to boil. Once sugar is dissolved, sieve into another container being sure to press on leaves with the back of a spoon. Good refrigerated to about 2 weeks.