Combine cilantro stems, white pepper, coriander, and garlic in a mortar and pestle and pound into a fine paste. This can also be done in a small food processor. In a large mixing bowl add fish sauce, oyster sauce, ground turmeric, brown sugar, and the prepared paste. Mix everything together well and add chicken. Toss until chicken is well coated. Add cover, and refrigerate for 1 to 2 hours. In a small bowl add lime zest, juice, cilantro, and the coconut milk until you have reached your favorite consistency. Add salt and pepper to taste. Thread the chicken pieces onto soaked bamboo skewers, pushing them tightly against each other to form a tight, compact body of meat on the skewers. Heat a cast-iron grill pan until very hot. Spray with canola oil before placing a few skewers at a time onto the pan. Grill the chicken, turning occasionally, until thoroughly cooked through and slightly charred, about 8 minutes total. Remove the chicken from the grill and serve with the coconut dip.