Boil 2 cups of water in a medium saucepan.

Remove from heat.

Mix in finely grated ginger and 1 teaspoon of lime juice.

Cover and let stand for 1 hour.

Add brown sugar and stir until dissolved.

Strain the ginger beer into a bowl, pressing firmly on solids to extract as much liquid as possible.

Cool completely.

Transfer ginger beer to a jar, cover, and chill for at least 2 hours or up to 1 week.

Mix rum, Simple Syrup (inferred), falernum, ginger beer, and the remaining lime juice in a pitcher.

Fill tall glasses with ice.

Pour the mixture over the ice.

Garnish the rim of each glass with a lime peel curl (optional).