Soak bamboo skewers in water for 30 minutes to prevent burning.
Mix the olive oil, lime zest, fish sauce, garlic, ginger and basil together. Season with salt and pepper.
Wash the monkfish under cold running water, and pat dry with kitchen paper. Add to the marinade and mix well. Cover and leave to marinate in the refrigerator for 2 hours, stirring occasionally.
Preheat a charcoal barbecue or grill until hot. Lift the monkfish pieces from the marinade, and thread them onto the skewers, alternating with the lime wedges.
Cook the skewers for 5–6 minutes on the hot barbecue or under the grill, turning regularly, until the fish is tender.
Serve with noodles or rice.