Pat the cod fillet dry with paper towels and season both sides with sea salt and freshly ground black pepper. Cut the broccoli into small florets. Scrub the half organic lemon clean, zest it, and squeeze out the juice. Chop the fresh dill finely.
Bring a small amount of water to a boil in a pan and place a steamer basket inside. Steam the broccoli florets with the lid closed for five to seven minutes until tender-crisp. Remove the broccoli from the pan immediately and set aside. Meanwhile, heat the olive oil in a skillet over medium-high heat. Place the cod in the pan and cook for three to four minutes on one side. Carefully turn the fillet and cook the other side for another two to three minutes until the fish is opaque and cooked through.
Remove the skillet from the heat. Pour the squeezed lemon juice directly over the warm cod fillet.
Place the cooked fish on a plate and arrange the steamed broccoli alongside it. Sprinkle the dish with the finely chopped dill and lemon zest and serve immediately.