Add coconut milk, red curry paste and brown sugar to a large bowl. Grate in the fresh ginger and stir in the salt. Remove one and a half cups of the marinade (before putting in the chicken!) and place it in a small bowl or jar. Keep this in the fridge until you're ready to grill your chicken.
Add the chicken pieces to the marinade and cover with plastic wrap. Let the marinated chicken sit in the fridge for at least 4 hours up to overnight.
Before grilling, pull the raw chicken out of the fridge. Let it sit on your countertop for 30 minutes to lose its chill. Meanwhile, preheat your grill over high heat.
Once the grill is hot, add your chicken pieces and drop the temperature to medium heat. Grill each piece until golden brown and slighly charred, flipping as needed. Once the internal temperature of the dark meat registers at 175-190 degrees F (or 165 degrees F for white meat) pull the chicken and plate it.
While the chicken is resting make the sauce. Add the reserved coconut curry sauce to a sauce pan over medium-high heat. Once the sauce starts to boil, turn it to medium-low heat and let it simmer, stirring often, and reduce until thick and glossy.
Before serving, pour the sauce over the chicken and top with chopped green onions and a squeeze of lime juice. Enjoy!