In a 4- to 5-quart pan over medium heat, melt butter. Add fennel, onion, and ginger. Stir often until fennel is tender when pierced, 8 to 10 minutes. Add 2 cups broth.
Pour mixture into a blender and add miso. Whirl until as smooth as you like. Return to pan and add remaining 4 cups broth. Stir often over medium-low heat until hot. Ladle into bowls, then add chives.