Rinse the rice and combine with 2 cups of the chicken stock in a medium pot. Bring to a boil then simmer until the liquid is absorbed and the rice is tender, adding water if necessary.
Add peas, if using, towards the end of cooking.
In the meantime, melt the butter in a saucepan over medium-low heat until the foam subsides.
Add the flour and whisk into the butter, breaking up any clumps.
Add the chicken stock, whisking. Bring to a boil, then simmer about 10 minutes.
Add the milk, nutmeg, cayenne, 2 tablespoons of the lemon juice, and salt to taste. Bring to a boil and simmer an additional 5 minutes.
Season the chicken breasts with salt and pepper and saute over medium heat until cooked through (alternatively, they can gently poach until cooked).
Add the final tablespoon of lemon juice to the rice and taste for seasoning. Slice the chicken and serve on the rice smothered in the sauce.
