In the bottom of a cocktail shaker, using a muddler or the handle of a wooden spoon, muddle the chopped fennel and 1/2 cup fennel fronds until well mashed, about 1 minute. Add the gin, lime juice, Green Chartreuse, and simple syrup. Fill the shaker with ice. Shake well (about 20 good shakes) and strain into 2 rocks glasses filled with ice. Top with seltzer. Garnish with fennel fronds.