Grind the spices and mix with the yogurt. Salt the chicken and put in a plastic bag. Pour in the yogurt marinade and massage it into the chicken.
Marinate (in the refrigerator) for 2-3 hours or overnight. If you are in a rush, marinate for at least 15 minutes at room temperature.
Put chicken and marinade in a slow cooker and cook on high heat for three hours or low for 6-8 hours. Remove and let cool. You can prepare up to this step a day ahead.
Prepare the grill and finish off the chicken with a nice browned surface, about 5-10 minutes on each side, depending on size and heat.
If you don’t have access to a grill, you can sear the boiled chicken in the oven using the broiler setting. Cut the limes in half and fry or grill alongside the chicken, cut side down. They add a wonderful flavor.
Boil the broccoli in lightly salted water; a minute or two is enough.
Mix the mayonnaise with freshly chopped cilantro and add the broccoli. Season with salt and pepper to taste.
Serve paired with the chicken, with an extra dollop of butter or mayonnaise on the side.