Remove the bones from the chicken thighs. For the marinade: Place the yogurt and the and the next ten ingredients in the bowl of a food processor. Process for about 1 minute or until you have a smooth puree. Place the chicken thighs in a large bowl, cover with the marinade, and marinate, refrigerated, for 24 hours. When ready to cook, remove the chicken from the marinade and pat completely dry with towels. Begin grilling the chicken. Place the pieces over a medium-high charcoal fire and cook for about 5 minutes per side. They are done when they're just past a rosy tinge at the center. Keep warm.
For the sauce: Puree 1 medium large onion (along with a little water) in a food processor. Melt 2 tablespoons. butter in a saucepan. Over medium heat, add onion puree and cook for 4-5 minutes.
Add 1 teaspoon cumin, 1 teaspoon coriander, 1/2 teaspoon garam masala, 1/2 teaspoon Indian chili powder, and 1 cinnamon stick. Blend. Add 1 tablespoon tomato paste and 1 cup chicken broth. Simmer for 1 1/2 hours. Add 1 tablespoon tandoori marinade and cook gently for 5 minutes. When ready to serve, strain over chicken tandoori.