Heat the oil in a 5-quart Dutch oven over medium-high heat. Add the onions and sauté until light golden in color, about 10 to 15 minutes.
Add the tomatoes, paprika, garlic and bay leaf. Reduce the heat, cover, and simmer until the tomatoes are soft and partially dissolved, about 15 minutes.
Pour in the wine and simmer for 2 more minutes. Add the chicken and water, adding extra water if needed to just cover the chicken. Recover the pot tightly and bring to a boil over medium-high heat. Reduce the heat and simmer the chicken for 15 minutes.
Add the rice, salt and pepper. Stir and continue to simmer for another 20 minutes.
Stir in the peas and 1 tablespoon of the parsley and simmer for 5 minutes more or until the meat is nearly falling off the bone.
Remove the pan from the heat. Let the stew stand for 10 minutes before serving. Garnish with remaining parsley. The rice should be tender and the liquid should be absorbed.