Bring water to a boil in a small saucepan. Add rice; reduce heat to low, cover and cook for 5 minutes. Remove from the heat.
Meanwhile, heat oil in a large nonstick pan over medium-high heat. Add turkey and ginger; cook, crumbling with a wooden spoon, until the turkey is cooked through, about 6 minutes. Stir in the cooked rice, bell pepper, water chestnuts, broth, hoisin sauce, five-spice powder and salt; cook until heated through, about 1 minute.
To serve, spoon portions of the turkey mixture into lettuce leaves, top with herbs and carrot and roll into wraps.
Hoisin sauce is a spicy, sweet sauce made from soybeans, chiles, garlic and spices. It will keep in the refrigerator for at least a year.Often a blend of cinnamon, cloves, fennel seed, star anise and Szechuan peppercorns, five-spice powder was originally considered a cure-all miracle blend encompassing the five elements (sour, bitter, sweet, pungent, salty). Look for it in the supermarket spice section.