Combine the coconut milk, soy sauce, brown sugar, lime juice, garlic and ginger in a large resealable bag. Add the chicken and toss to coat. Marinate in the refrigerator for at least one hour, up to 8 hours.
Heat an outdoor grill, indoor grill pan or skillet over medium-high heat. Season the chicken on both sides with salt and pepper, place on grill/skillet and cook for 5-6 minutes on each side or until done. Cut the cooked chicken into cubes (approximately 1/2 inch in size)
For the peanut sauce:
Combine all of the ingredients in the food processor and process until smooth. Add salt and pepper to taste.
Warm the tortillas in the microwave. Place the tortillas in a row assembly line style. To each tortilla add 2 tablespoons of shredded cabbage, 1 tablespoon of shredded carrots, 1 tablespoon of cucumber and approximately 1/4 cup of chicken. Top with a generous drizzle of peanut sauce and a few cilantro leaves. Serve immediately with lime wedges if desired.
Make Ahead: The carrots and cabbage can be shredded a day in advance. The peanut sauce can be made up to 3 days in advance.