Cut the fennel bulb in half lengthwise and then cut each half lengthwise into four 1-1/2-inch-thick wedges. Trim a little of the core but leave enough to hold the layers together.
With a pairing knife, slice the olive flesh off the pits lengthwise.
In a 12-inch skillet, heat the olive oil over medium-high heat. Add the fennel, one cut side down, and reduce the heat to medium. Cook, turning once with tongs, until the wedges are lightly browned on both cut sides, 2 to 3 minutes per side. Add the onion and salt. Cook, stirring occasionally and gently so as not to break up the fennel wedges, until the onions are slightly softened and browned, about 5 minutes.
Add the tomatoes, capers, and olives to the pan along with 1 cup water. Bring to a simmer, cover, and reduce the heat to medium low or low, to maintain a steady simmer. Cook until the fennel wedges are fork tender, 20 to 25 minutes. Uncover, raise the heat to high, and simmer briskly until most of the liquid evaporates, leaving a thick sauce, 3 to 5 minutes. Gently stir in the parsley. Let rest 15 minutes before serving.
Serve with grilled swordfish or tuna, roast chicken, or grilled sausages.