Melt the butter in a large heavy pot over low heat. Add the onion,carrots and curry powder and cook,covered, until the vegetables are tender, about 25 minutes; stir occasionally.
Add the stock,parsley, chicken and rice. Bring the soup to a boil,reduce the heat,and cover. Cook at a simmer until the chicken is done, skimming any foam from the cooking liquid as necessary, 25 to 30 minutes.
Cook the chicken in the stock. Remove the meat from the bones and dice it; reserve the meat.
Pour the soup through a strainer and transfer the solids to a food processor or use a food mill fitted with a medium disc. Add 1 cup of the cooking liquid and process until smooth. Reserve the rest of the liquid.
Return the pureed soup to the pot and add the half and half. Stir in about 4 cups more cooking stock,until the soup reaches the desired consistency.
Add the reserved diced chicken and defrosted peas and simmer the soup until the peas are tender, 15 minutes. Season with salt and pepper and serve immediately.