In a pan over medium heat, heat the olive oil. Cook until the onion, bell peppers, and garlic are transparent. Add the tomato, bay leaf, paprika, saffron, salt, and pepper to taste.
Cook for 5 minutes, stirring occasionally. Cook for 10 minutes after adding the white wine. If necessary, season with salt.
To the saucepan, add the chicken pieces, 2 tablespoons minced parsley, and rice.
Pour the broth slowly around the pan, jiggling the pan to get a uniform covering of rice. (Do not continue to stir the mixture!)
Bring the liquid to a boil. Turn the heat down to medium-low. During cooking, give the pan a slight shake back and forth once or twice. (We never stir the rice so that a crispy crust forms at the bottom, which is known as a socarrat.)
Simmer for approximately 15-18 minutes (uncovered), then nestle the shrimp, mussels, and calamari into the sauce, sprinkle with peas and cook for another 5 minutes (without stirring).
Keep an eye out for most of the liquid to be absorbed and for the rice on top to be nearly tender. (If your rice is still uncooked, add 1/4 cup additional water or broth and continue cooking.)
Remove from the heat and cover with a lid or tinfoil. Cover the lid with a kitchen towel and set aside for 10 minutes.
Garnish with lemon slices and fresh parsley. Serve.