Ready a fairly large heavy-bottomed skillet and accompanying lid. This is for the vegetables. Heat the pan to medium-high.
Now, start the vegetables. Add 1 tablespoon olive oil to the pan. Add onion, bell pepper, and sliced garlic. Sauté 6 minutes or until the vegetables are lightly browned and wilted.
Lower the heat to medium-low. Add the piquillos and the tomatoes. Cover and cook for about 20 minutes.
Heat a medium-sized skillet to medium-high. Pat the cod fillets dry with paper towels. Season with the salt.
Add 1 tablespoon olive oil to the medium-sized skillet, and add the seasoned fillets to the pan. Press gently to ensure that the surface area of the fish touching the pan is free of air pockets. Cook for about 3 minutes before attempting to turn.
Cook the flip side of the fish roughly 5 minutes, depending upon thickness, just until fish flakes evenly when tested with a fork but retains some translucency--a glisten. Cod is a fish that can carry-over cook quite fast, and if you cook it 100% through at the stove, it will be dry at the table. For sure. Turn off the heat and let the cod rest in the pan.
When the vegetables are tender, remove the lid and raise the temperature to high. Reduce most of the liquid out of the pan. It should glisten and be almost jammy in texture. Now, fold in the espelette pepper and the olives.
Raise the heat on the cod pan to low. Spoon the entire tomato-pepper-olive mixture over the cod fillets and warm the pan until it bubbles and/or sizzles. Sprinkle with parsley. Serve.