Combine the rice, 2 cups of water and a pinch of salt in a saucepan and bring to a simmer. Cover, reduce heat to low, and simmer until the grains are tender, about 20 minutes.
Bring a large pot of salted water to a boil for the green beans. Prepare an ice bath by filling a large bowl with cold water and ice. When the water boils, add the green beans for 2 to 4 minutes, until bright green. then immediately transfer to the ice bath to stop the cooking process. Remove from the ice bath after 1 to 2 minutes.
In a large skillet, heat the oil. Add the shrimp and cook, stirring, until no longer pink. Remove to a plate. Add the bell pepper and mushrooms and cook until softened. Stir in the curry paste and cook until fragrant, about 1 minute. Add the coconut milk, chicken stock, fish sauce, brown sugar, lime leaves, salt and pepper and bring to a simmer. Reduce the heat and simmer for 10 minutes. Stir in the green beans and chicken.
To serve, divide the rice and curry between plates.