1/2 cup pitted and roughly chopped large green olives, such as Cerignola (about 6)
3/4 cup canned chickpeas, rinsed and drained
Preheat oven to 350 degrees. In a large ovenproof skillet or Dutch oven, heat olive oil over medium heat. Place chicken pieces in skillet. Do not over crowd the pan with chicken. Saute until chicken is nicely crisped and browned on both sides, about 5 minutes per side. Transfer chicken to a large plate, and set aside.
Using the same skillet; reduce heat to medium-low. add onion, carrots, garlic, and ginger. Saute, stirring frequently, until onion is soft and translucent, about 5 minutes. Add chicken broth, water, and wine; bring to a boil, and deglaze pan by scraping up any browned bits from the bottom with a wooden spoon. Return chicken to skillet, and add thyme. Bring liquid back to a boil; cover, and transfer to the oven. Braise 45 minutes.
Remove skillet from oven, and stir in raisins, olives, and chickpeas. Return to oven; continue braising, uncovered, 20 minutes more. Remove from oven, and discard thyme. Serve hot.
Preheat oven to 450 degrees. Rub baking sheet with oil. Place tomatoes, garlic, and 1 tablespoon olive oil in a food processor; season with salt and pepper. Pulse 3 to 4 times until ingredients are incorporated but chunky.
On a lightly floured work surface, use a rolling pin and your hands to roll and stretch dough until large enough to cover the surface of the baking sheet. Transfer to prepared baking sheet.
Spread tomato sauce over dough, leaving a 1-inch border all around. Top with cheese and pine nuts; season with salt and pepper.
Bake until crust is golden, 15 to 20 minutes. Toss arugula with vinegar and 1 tablespoon oil; season with salt and pepper. Sprinkle arugula and olives over pizza.