Heat oven to 400° F. Heat 1 tablespoon of the oil in a large ovenproof skillet over medium-high heat. Add the sausage and cook, tossing occasionally, until browned, 2 to 3 minutes.
Add the potatoes and cook, stirring occasionally, for 10 minutes. Add the leeks, saffron, ½ cup water, ¾ teaspoon salt, and 1/8 teaspoon pepper. Bring to a boil.
Season the cod with ½ teaspoon salt and 1/8 teaspoon pepper. Place it on top of the potatoes and drizzle with the remaining tablespoon of oil.
Transfer the skillet to oven and bake until the cod is opaque throughout, 15 to 20 minutes. Sprinkle with the parsley before serving.