For the tandoori powder, combine all the ingredients and store in an airtight container at room temperature (the above recipe makes about 3/4 cup). For the tahini dressing, combine all the ingredients and adjust the dressing's consistency with more or less water and store, covered, in the refrigerator for up to 1 week (makes about 3/4 cup).
Preheat a gas grill to high (or prepare the coals for a charcoal grill). In a large mixing bowl, toss the chicken with the tandoori powder and oil to evenly coat the meat. Arrange the chicken on the grate and grill, turning as needed, until cooked through, about 8 minutes total. Move the chicken to a plate.
While the chicken is cooking, cut the carrots into ribbons by running a vegetable peeler straight down each carrot from stem to root. After you've cut about halfway through the carrot, flip it over to cut down the other side.
Divide the carrot ribbons among the serving plates and drizzle each with about 1 tablespoon tahini dressing. Garnish each salad with some herbs and cashews (if using) and serve with the grilled chicken.