In a bowl or large zip-top bag, combine soy sauce, water, brown sugar, minced garlic, grated ginger, sesame oil, coconut milk, and pineapple juice, stirring until the sugar dissolves completely. Add the chicken thigh strips and ensure they are fully submerged in the marinade. Cover and refrigerate for at least 2 hours, though up to 24 hours will develop deeper flavor. I find that even 4-6 hours gives excellent results if you're short on time, so don't stress about hitting the full 24 hours.
In a medium pot, combine coconut milk, water, and salt, and bring to a boil over medium-high heat. Add jasmine rice, stir once, then reduce heat to low, cover with a lid, and cook for 18 minutes until the liquid is absorbed and rice is tender. While the rice cooks, you'll have time to prepare the grill and pineapple, so this step ensures everything finishes around the same time.
Preheat your grill to medium heat (around 375-400°F) for about 10 minutes while you pat the pineapple rings dry with paper towels. Dry pineapple grills much more evenly and develops better caramelization. Remove the chicken from the marinade, letting excess marinade drip back into the bag, and arrange the pieces on a plate near the grill.
Place the marinated chicken strips on the grill and cook for 6-7 minutes on the first side without moving them, allowing a nice char to develop. Flip and cook for another 6-7 minutes on the second side until cooked through. During the final 3-4 minutes of chicken cooking, place the pineapple rings on the grill and cook for 2-3 minutes per side until they have light char marks. I like to brush the pineapple lightly with any remaining marinade before grilling to add extra flavor and prevent sticking.
Remove the rice from heat and stir in the brown sugar, gently fluffing with a fork. The rice should be fluffy and the sugar should dissolve from the residual heat. Transfer the grilled chicken and pineapple to serving plates, add a generous portion of coconut rice alongside, and garnish with toasted sesame seeds and fresh cilantro. Serve with lime wedges on the side for squeezing over everything.