Jamaican Rum-Ginger Zinger

2 cups water
2 oz fresh ginger
3/4 cup+ 1 tsp, fresh lime juice
1 tbsp(packed) golden brown sugar
1 1/2 cups dark rum
3/4 cup simple syrup
1/4 cup falernum syrup

Bring 2 cups water to boil in medium saucepan. Remove from heat. Mix in grated fresh ginger and 1 teaspoon lime juice. Cover and let stand 1 hour. add brown surgar; stir to dissolve. Strain ginger beer into bowl, pressing firmly on solids to extract as much liquid as possible (mixture will be cloudy). Cool completely. Transfer ginger beer to jar. Cover and chill at least 2 hours or up to 1 week. Mix rum, Simple Syrup, falernum, ginger beer, and remaining 3/4 cup lime juice in pitcher. Fill tall glasses with ice. Pour mixture over. If desired, garnish rim of each glass with lime peel curl.