Preheat the oven to 350 degrees. In a 10-inch paella pan or ovenproof skillet, cook the chorizo over moderate heat, breaking it up with a spoon, until some of the fat is rendered and the chorizo is browned, 4 minutes. Add the onion and garlic and cook over low heat, stirring, until softened and just beginning to brown, 8 minutes. Stir in the tomatoes, rice, saffron with its liquid, and the 1 1/2 cups of water. Season with salt and pepper and bring to a boil. Cover and simmer over low heat, without stirring, until the rice is al dente and the liquid is absorbed, 15 minutes.

In a large skillet, heat the 1/4 cup of olive oil until shimmering. Season the shrimp with salt and pepper, add them to the skillet and cook over high heat, turning once, until pink and cooked through, about 3 minutes. Using a slotted spoon, transfer the shrimp to the rice. Discard the oil.

Wipe out the skillet. Pour in the wine and lemon juice. Add the mussels and cockles, cover and cook, shaking the skillet, until the mussels open, about 3 minutes. Pour the mussels and cockles and their cooking liquid over the rice.

Stir the cooked chicken into the rice. Cover and cook in the oven for about 5 minutes, until the paella is just heated through. Garnish with the parsley and scallion, drizzle with the remaining 1 tablespoon of olive oil, and serve.