If you haven't already, make our romesco sauce.
Pat cod fillets dry with a paper towel, then season on both sides with 1 tsp Kosher salt and ¼ tsp black pepper.
Heat oil over medium-high heat in a large skillet. When hot, add seasoned cod fillets, leaving a little space between each. Cook until light golden brown. Use a fish spatula to carefully flip each piece of cod over. Add unsalted butter to the pan, and as soon as it begins to melt, use a spoon to base some of the butter over the cod. Cook.
Transfer cod fillets to one large serving tray or individual plates, then spoon some of the romesco sauce on top. Garnish with freshly parsley, then serve immediately!