For the marinade:
- Put the ginger and garlic in a food processor or Cuisinart Mini Prep. Whirl until finely minced. Transfer to a bowl large enough to hold the chicken thighs. Add coconut milk, chili paste, lime zest, lime juice, brown sugar, salt and olive oil. Whisk to mix.
For the chicken:
- Add chicken to the bowl of marinade and toss with your hands to thoroughly coat. Allow to marinate 1 to 4 hours.
- When ready to cook, heat the grill to medium. Using your hands wipe off excess marinade from the chicken and grill until done, about 10 minutes total, flipping occasionally. Reserve leftover marinade.
For the sauce:
- While the chicken is grilling, put the residual marinade in a saucepan and bring to a full boil for 1 minute. Reduce heat to medium and continue to cook until the sauce is reduced to about one third its original volume, stirring frequently. Sauce will be thick, but still pourable.
To serve:
Plate the chicken on a large platter, drizzle with sauce and garnish with lime wedges and cilantro leaves. Serve hot or room temperature.