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Bring water and rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and water has been absorbed, 20 to 25 minutes; set aside.
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Heat oil in a skillet over medium heat. Add chicken; cook until chicken is no longer pink at the center and juices run clear, about 5 minutes. Transfer to a plate and cover to keep warm.
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Add a small amount of additional oil to the pan if needed, then add onion. Saute until onion starts to soften, about 3 minutes. Sprinkle on coriander and stir through.
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Add peanut butter, chili flakes, broth, lime juice, and bouillon. Cook and stir until thickened, about 4 minutes.
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Add chicken plus any accumulated juices from the plate, and stir to coat completely. Serve over rice in small bowls; sprinkle with green onion.