Heat 2 tablespoons oil in a large skillet over medium heat. Season the chicken with salt and pepper and cook until browned all over, adding more oil to the pan if necessary. Add the chorizo and cook for 1 minute. Add the garlic and paprika and cook for another 2 minutes.
Take the pan off the heat and add half the sherry, if using. Return the pan to the heat and bring to a boil. Cook until the sherry has almost evaporated. Add the rice, saffron, butter and stock. Add a bit more stock if you did not use the sherry. Turn the heat down and simmer for 30 minutes, or until most of the liquid has been soaked up by the rice. Do not mix the rice, as it will be a lovely crunchy layer on the bottom. 15 minutes into this cooking time, cover the pan with a lid, baking sheet or aluminum foil. When done, remove the pan from the heat.
While the rice is cooking, heat 1 tablespoon oil in a medium skillet. Add the scallions and cook just until they start to color, about 2 minutes. Add the shrimp and cook until they turn pink, 2 to 3 minutes. Add the peas and cook until they are warmed through, 2 to 3 minutes. Remove the pan from the heat and add the remaining sherry, if using. Return to the heat and cook until most of the sherry has evaporated. Pour the shrimp and peas over the cooked rice mixture.
Serve while hot, garnished with parsley and lime wedges.