Heat oil in a small frying pan. Add garlic and ginger. Saute till fragrant, about 1 minutes. Add Garam Masala, cumin, and chili powder. Saute for another minute till fragrant. Remove from heat.
Place half of the spice mixture in a bowl big enough to hold the yogurt. Add the yogurt and two tablespoons of the lime juice. Set aside.
Trim the thighs and cut a 1/8 inch deep slice, twice, across each thigh.
Combine the remaining spice mixture with the salt and the remaining lime juice in a bowl big enough to hold all the chicken. Massage the spice mixture into and all around the chicken thighs... Allow to sit for at least a half hour.
Preheat BGE to 500 degrees
Add the yogurt mixture to the chicken and stir to coat each piece.
Place on rack, direct heat.
Turn after about 5 minutes. Cook another 5 minutes or till internal temperature reaches > 150. Serve with nan and lime slices. You want a few dark or charred areas on the chicken.
Place the water, salt, and yeast into the TM. Process at speed 4 for about 10 seconds or till the salt and sugar are dissolved.
Add the egg, and process another 2 seconds at speed for to mix in the egg.
Add the remaining ingredients, starting with the yogurt. Process for 7 minutes on intermittent speed.
Place dough in a greased bowl and allow to rise till doubled in bulk (about an hour).
Portion the dough into 8 equal balls. Allow to rest for 10 or more minutes.
Flatten the dough balls into pancakes about a quarter inch thick, and brush tops with some more ghee. Bake on a pizza stone (4 should fit on at a time) preheated to 500, about 4 to 5 minutes per side, or until desired color is reached.
Here's the nan served with tandoori chicken.