Step 1

Preheat oven to 375°F. Heat oil in a 12-inch skillet over medium-high. Sprinkle chicken with 2 3/4 teaspoons salt and 1 teaspoon black pepper. Working in batches if needed, cook chicken in oil, turning occasionally, until golden brown on both sides, 8 to 12 minutes; transfer to a large plate. Add garlic head halves, cut sides down, to skillet; cook, undisturbed, until lightly browned, about 30 seconds. Transfer to plate with chicken.

Step 2

Remove skillet from heat, and immediately add fennel seeds to drippings. Off heat, stir constantly until fragrant, about 30 seconds. Add broth, sherry, olive brine, chile oil, remaining 3/4 teaspoon salt, and remaining 1/4 teaspoon black pepper. Using a wooden spoon, scrape up any browned bits from bottom of skillet. Arrange chicken leg quarters, skin sides up, in skillet. Tuck browned garlic halves, fennel wedges, and orange and lemon slices in skillet around chicken. Sprinkle with olives and chiles.

Step 3

Bring liquid in skillet to a boil over medium-high. Cover skillet tightly with aluminum foil, and transfer to preheated oven. Roast until a thermometer inserted in thickest portion of chicken registers 130°F, 35 to 40 minutes. Remove foil, and roast until chicken registers 165°F and fennel is tender, 15 to 20 minutes. Remove from oven. Sprinkle with pre-served lemon peel, and garnish with fennel fronds. Serve with torn baguette.