Preheat the oven to 400°F (200°C). Generously spray a glass or ceramic 9×13-inch baking pan; do not use metal.
Open the can of coconut milk without shaking. Scoop out about 1/3 cup of the thick coconut cream into a small blender or food processor and set aside. Pour the remaining coconut milk (liquid) into the prepared baking pan.
Add the uncooked basmati rice, chicken stock, soy sauce, 1 tablespoon olive oil, ginger paste, minced garlic, 1/2 teaspoon salt (or to taste), the unthawed edamame, and the unthawed corn to the pan with the coconut milk. Stir until evenly combined and spread into an even layer.
Cover the pan tightly with aluminum foil and bake for 40 minutes. After 40 minutes, remove the foil and bake uncovered for an additional 15 minutes.
While the rice bakes, shred or chop the cooked chicken into small pieces.
Make the cilantro‑jalapeño lime sauce: combine the reserved 1/3 cup coconut cream, remaining 2 tablespoons olive oil, cilantro, chopped jalapeño, 1 teaspoon lime zest, 3 tablespoons lime juice, and about 1/4 teaspoon salt in the blender. Pulse until cilantro is broken down and the sauce is just combined; do not overblend. Chill until ready to serve.
After the final 15 minutes of baking, remove the dish from the oven. Do not stir. Sprinkle the shredded chicken evenly over the rice. Drizzle the remaining 1 teaspoon lime zest and 2 tablespoons lime juice over the chicken and rice. Cover again with foil and let the pan stand at room temperature for 10 minutes.
After 10 minutes, gently mix the chicken into the rice and lightly fluff with a fork. Serve portions topped with the cilantro‑jalapeño lime sauce and optional toppings as desired.