Light a grill or preheat a grill pan. In a medium bowl, combine the ground lamb with the cooked rice, egg and 1/4 cup of the cilantro. Add 1 teaspoon of kosher salt and 1/2 teaspoon of black pepper and gently knead the meat to blend. Using lightly moistened hands, form the meat into 12 patties, about 1/2 inch thick. Brush the patties with olive oil.
Grill the patties over moderate heat, turning occasionally, until browned and cooked through, about 6 minutes.
Meanwhile, in a food processor, combine the hot and mild chiles with the scallions, garlic and the remaining 1/4 cup of cilantro and pulse until chopped. Add the 1/4 cup of olive oil and process to a chunky puree. Season the harissa with salt. Wrap the lamb in the warm naan with tomatoes and feta. Spoon some of the green harissa on top and serve.