With a sharp paring knife, make 2 to 3 (1/2-inch deep) diagonal cuts in each piece of chicken, being careful not to cut all the way through.
In a small saute pan set over moderate heat, combine the ginger, cumin, coriander, paprika, turmeric, cardamom pods, and cayenne. Cook, gently shaking the pan, until you can smell the spices, approximately 1 minute.
Transfer the spices to a spice/coffee grinder and grind the spices finely.
Transfer the chicken pieces to a large resealable plastic bag and add the spice mixture, garlic, and lemon juice and toss to coat thoroughly, making sure the rub penetrates the cuts. Marinate the chicken in the refrigerator, for at least 5 hours or overnight.
Remove chicken pieces from the plastic bag and pat them dry. Season with salt and pepper, to taste. Rub the chicken pieces thoroughly with half the shortening.
Grill chicken on an oiled rack 5 to 6 inches over glowing coals or on a gas grill for 7 to 10 minutes per side. While grilling, brush on the remaining shortening. When the chicken pieces are cooked through, transfer to a platter. Let chicken stand while preparing salad.
In a sieve, drain the yogurt for 15 minutes. In a bowl, combine yogurt, lemon zest, lemon juice, garlic, cilantro, cayenne, salt, and pepper, to taste.
In a large bowl, whisk together the pressed garlic, lime juice, fish sauce, and sugar, and blend until the sugar is dissolved.
Add chile, papaya, carrot, and cilantro to the dressing, tossing well. Salad may be made 2 hours ahead and chilled, covered. Bring salad to room temperature before serving. Serve salad sprinkled with peanuts.