1. Trim the stem end and the dark green tops from the fennel; reserve a few fronds for garnish. Cut the fennel bulb lengthwise into quarters; then cut across into 1-inch pieces. Chill in a bowl of iced water for 20 minutes; drain.

2. Meanwhile, bring a small pan of water to a boil. Place the figs in a small bowl and cover with boiling water; let stand for 10 minutes. Drain, and cut the figs in half

3. Sprinkle the chicken pieces with salt and pepper. Heat the butter and olive oil in a large deep skillet until sizzling. Add the chicken, a few pieces at a time, and cook until lightly browned, about 5 minutes per side. As it browns, transfer the chicken to a side dish. Leave a thin film of oil in the bottom of the pan: discard any remaining oil.

4. Add the fennel, leeks, and carrots to the pan. Cook, stirring, until the vegetables have softened, about 5 minutes. Add the figs and fennel seeds to the pan. Cook, stirring, until the cut sides of the figs are lightly browned, about 5 minutes. Add the garlic and cook, stirring, for 1 minute.

5. Add the chicken broth and the wine and heat to a boil. Boil, uncovered, over high heat until the liquid is reduced by half, about 5 minutes. Add the cooked chicken and any accumulated juices to the pan. Cover and cook over medium-low heat until the chicken juices run clear when the flesh is pierced with a fork, about 15 minute.

6. Using a slotted spoon, transfer the chicken, vegetables, and figs to a warmed serving platter; cover to keep warm. Boil the juices over high heat until reduced and slightly thickened, 1 to 2 minutes. Pour the juices over the chicken; garnish with the reserved fennel fronds, and serve.