In a medium bowl, whisk together the grated ginger, minced garlic, coconut milk, chili paste, lime juice, brown sugar, salt, and vegetable oil until well combined.

Place the chicken thighs in a large zip-top bag or shallow dish. Pour the marinade over the chicken, ensuring each piece is well coated. Seal the bag or cover the dish, then refrigerate for at least 15 minutes or up to 4 hours.

Before grilling, transfer the leftover marinade to a small saucepan. Bring it to a boil, then reduce the heat to medium-low. Simmer until the sauce thickens enough to coat the back of a spoon (about 2-3 minutes). Set aside.

Preheat your grill to medium heat. Clean and generously oil the grill grates to prevent sticking.

Remove the chicken from the marinade, letting excess drip back into the dish. Place the chicken on the grill and cook for 8-10 minutes, turning once, until you see grill marks and the chicken is fully cooked.

Baste the chicken occasionally with the reserved marinade for extra flavor.

Transfer the grilled chicken to a serving platter. Drizzle or brush with any remaining sauce. Garnish with cilantro leaves and serve with lime wedges. For a complete meal, serve alongside white rice and sautéed zucchini.