Trim off the root, the dark greens, and most of the light green parts of the leeks. Chop the leeks into 1/2-inch pieces and rinse thoroughly to remove all the grit. Cut the chorizo in half lengthwise and slice into half moons about 1/8 inch thick.
Put the potatoes in a large saucepan and cover with cold water by 1 to 2 inches. Salt the water, cover partially, and bring to a boil over high heat. Reduce the heat as needed and boil until the potatoes are tender, 10 to 15 minutes; drain. While the potatoes cook, heat the oil in a large pot (choose one that’s wide enough to hold the fish in a single layer) over medium heat for 1 minute. Add the chorizo and leeks and cook, stirring occasionally, until the chorizo has browned slightly and the leeks are soft, about 6 minutes. Add the garlic and cook for 1 minute. Stir in the tomatoes and their juices, the wine, 1-1/2 cups water, and 1/2 tsp. salt. Bring to a boil over high heat. Partially cover the pot, reduce the heat to medium, and simmer for 15 minutes. Add the potatoes, season with salt and pepper, and stir in half of the parsley. Season the cod with salt and pepper, set the fillets on top of the stew, cover, and simmer until just cooked through, 6 to 8 minutes. Using a wide spatula, carefully transfer the cod to shallow soup bowls (the fillets may break apart). Spoon the stew over the cod and serve immediately, garnished with the remaining parsley.