For the Ginger Syrup:
In a blender, purée the ginger, sugar, and water together for 15 minutes on high speed. Steep 15 minutes and strain through cheesecloth.
For the Fruit Cup:
In a cocktail shaker with ice, combine the gin, lemon juice, Americano, ½ ounce Ginger Syrup, aromatic bitters, and orange bitters. Shake gently. Strain over fresh ice, top with seltzer, and garnish with grapefruit twist and mint.