Preheat the oven to 375°F (190°C).
Place saffron threads in a small bowl with warm water and let soak for 10 minutes to release color and flavor.
In a small skillet, heat 1 tablespoon of olive oil over medium heat. Add the chopped shallot and garlic, sautéing until softened and fragrant, about 2-3 minutes. Remove from heat.
In a mixing bowl, combine the sautéed shallot and garlic, saffron water (including threads), lemon juice, lemon zest, 2 tablespoons olive oil, salt, and black pepper. Stir well to create the saffron lemon sauce.
Place the cod fillets in a baking dish. Spoon the saffron lemon sauce evenly over each fillet.
Bake in the preheated oven for 15-20 minutes, or until the fish is opaque and flakes easily with a fork.
Remove from the oven and sprinkle with chopped fresh parsley before serving.
Serve immediately, optionally accompanied by steamed vegetables or a light salad.