Place the 2 large potatoes, peeled and halved in a large pot of water, bring the water to a boil. Let the potatoes cook until they are almost tender. Add 1 pound cod fillets, cubed to the pot and let the fish and potatoes cook until they are both soft. Drain well and transfer the potatoes and fish to a large mixing bowl. Add 1 tbsp butter, 1 tbsp grated onion, 1 tbsp grated parsley, and 1 egg to the bowl; mash the mixture together. Mold the mixture into patties. Heat oil in a large skillet over a medium-high heat. Fry the patties on both sides until golden brown. Drain on paper towels before serving.