Cut each chicken thigh in half. Add the chicken to a medium bowl with the marinade ingredients and mix well. Set aside for 15 minutes while you prepare the remaining ingredients.
Peel and cut the potatoes into 1-inch cubes. Bring a medium pot of water to a boil over high heat. Add the potatoes and boil for about 5 minutes or until fork-tender. Drain and set aside.
Preheat the oven to 500°F.
Heat 2 tablespoons (30 ml) vegetable oil in a large pan over medium-high heat. Add the cold rice and break up any clumps. Add the soy sauce and eggs and stir-fry until the eggs are cooked and the rice grains are separated. Transfer the fried rice to a deep 9 × 13-inch baking dish and spread it into an even layer.
Heat 1 tablespoon (15 ml) vegetable oil in the same pan over medium-high heat. Add the diced onions and sauté until softened. Add the marinated chicken in a single layer and brown on both sides, about 4-5 minutes per side.
Add the cooked potatoes, coconut milk, turmeric, curry powder, and salt. Stir well and simmer uncovered for 2-3 minutes until the sauce is thick enough to coat the back of a spoon but isn't overly thick.
Pour the chicken and coconut curry sauce evenly over the fried rice, then sprinkle the shredded cheese evenly over top.
Bake at 500°F until the cheese is completely melted and lightly browned, about 5-10 minutes, watching closely to prevent burning. Remove from the oven and let it cool slightly before serving.