How to Make It
Preheat oven to 425°F with 1 oven rack in middle of oven and another in the top third of oven. Toss together clementine and lemon halves, shallots, and oil in a large deep ovenproof skillet. Spread in a single layer.
Stir together butter, zest, rosemary, thyme, salt, and pepper in a small bowl. Place chicken, breast side down, on a cutting board. Using kitchen shears, cut along both sides of the backbone, separating the backbone from the chicken. Remove and discard backbone. Turn chicken, breast side up, and press firmly to flatten. Rub butter mixture under skin and all over outside of chicken. Place atop fruit and shallots in skillet.
Bake in preheated oven until a meat thermometer inserted in thickest portion of the thigh registers 165°F, 50 minutes to 1 hour, shielding with aluminum foil to prevent excessive browning, if necessary.
Remove skillet from oven; transfer chicken to a cutting board, and tent with foil. Increase oven temperature to broil. Place skillet on top oven rack, and broil clementine and lemon halves and shallots until brown in spots, 3 to 4 minutes. Arrange chicken, clementines, lemons, and shallots on a serving platter; drizzle with pan juices.