Prepare the Marinade: In a food processor or blender, combine yogurt, cilantro, lime zest and juice, turmeric, cumin, salt, coriander, garam masala, black pepper, cayenne, onion, jalapeño, ginger, and garlic. Blend until smooth.
Marinate the Chicken: Use a sharp knife to slash each chicken piece to the bone in one or two places, allowing the marinade to penetrate deeply. Place the chicken in a large bowl and pour the marinade over it. Turn the pieces to coat them thoroughly. Cover the bowl with plastic wrap and refrigerate for at least 6 hours or overnight.
Preheat the Oven: Preheat the oven to 450°F.
Roast the Chicken: Line a rimmed baking sheet with aluminum foil. Transfer the chicken pieces from the marinade to the prepared baking sheet, and drizzle with oil. Roast the chicken, turning the pieces after 15 minutes and basting occasionally, until the juices run clear and the meat is just cooked through (about 25 to 30 minutes total).
Serve: Serve the chicken hot, garnished with Indian pickle, mango chutney, and lime wedges. Add basmati rice, yogurt, and fresh cucumbers or tomatoes on the side if desired.