Trim tough outer leaves from fennel; mince feathery fronds to measure 2 tablespoons. Remove and discard stalks. Cut fennel bulb in half lengthwise; discard core. Chop bulb to measure 1 cup.
Slice quartered potatoes into 1/4-inch-thick slices. Melt butter in a Dutch oven over medium-high heat. Add chopped fennel bulb, potatoes, and leek, and cook 3 minutes. Add water, salt, and broth, and bring to a boil. Cover, reduce heat, and simmer 25 minutes or until potatoes are tender.
Remove 2 cups of soup from pan. Place in a blender; process until smooth. Return pureéd mixture to pan, and stir in fennel fronds, parsley, and pepper. Spoon into bowls; top with sour cream.