In a medium saucepan, mix the rice with 2 cups water and a pinch of salt; bring to a boil. Reduce the heat to low, cover, and simmer about 15 minutes, or until the rice is cooked; set aside.
Meanwhile, in a large skillet, heat the butter over moderate heat. Add the flour and stir together to make a paste; let cook for about 1 minute. Slowly whisk in the chicken soup (reserve vegetables and chicken) or broth and let simmer for about 5 minutes, or until it thickens.
In a small bowl, beat the egg yolk, cream, another pinch of salt, and freshly ground black pepper. Add a few tablespoons of the simmering broth from the skillet and slowly whisk it in; add back to the skillet. Add the vegetables from the soup, if using soup instead of broth, then add the chicken to the skillet.
Reduce heat; add lemon juice. Taste sauce for seasoning; add more salt, pepper, or lemon juice to taste, if needed. Serve with the rice.
How kids can help: Measure ingredients; add lemon juice and seasonings to taste.
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