Chop enough fennel fronds to measure 2 tablespoons, then cut off and discard stalks from bulb. Quarter bulb lengthwise and core, then cut lengthwise into 1/4-inch-thick slices.
Cook fennel, onion, pepper, and 1/2 teaspoon salt in oil in a 12-inch heavy skillet over moderate heat, covered, stirring occasionally, until onion is softened, about 5 minutes.
Meanwhile, cut potatoes crosswise into 1/4-inch-thick slices.
Add potatoes and remaining 1/2 teaspoon salt to fennel mixture and cook, uncovered, stirring frequently, 3 minutes. Add water and cook, covered, stirring once, until potatoes are tender, 10 to 12 minutes more. Stir in fennel fronds before serving.