Stir together oil, lemon juice, salt, pepper, cumin, paprika, garlic, and cilantro in a medium bowl to make charmoula. Transfer 6 tbsp. to a small bowl.
Pull off tenders (the long, small, tenderloin muscles) from chicken. Add chicken (including tenders) to charmoula in medium bowl and turn to coat. Chill chicken and extra charmoula, covered, about 1 hour and up to 1 day, turning chicken once.
Heat grill to high (450° to 550°). Grill chicken, covered, turning once, until cooked through, 4 to 10 minutes; discard marinade. Transfer chicken to a board, let rest briefly, then slice diagonally. Grill rolls, cut sides down, until toasted, 1 minute.
Spoon 2 tbsp. reserved charmoula into a clean medium bowl, add carrot and pea shoots, and toss gently. Spoon 1 1/2 tbsp. more charmoula into a small dish and set aside. Whisk mayonnaise into charmoula remaining in the small bowl and spread over cut sides of the rolls.
Fill rolls with pea shoot salad and arrange chicken on top. Spoon about 1 tsp. reserved charmoula (from small dish) over chicken on each sandwich.
*Find at farmers' markets or Asian markets.
Note: Nutritional analysis is per sandwich.