Rinse the salt cod under cold water.

Place the fillets in a bowl and cover with cold water.

Refrigerate, changing the water occasionally, for about 24 hours until the fish is soft.

Place the potatoes in a pot and cover with lightly salted water.

Bring to a boil and cook until the potatoes are soft.

Drain the potatoes, mash them, and set aside.

Drain the salt cod fillets and shred them into a bowl.

Add the mashed potatoes, chopped onion, egg yolks, minced garlic, chopped parsley, and olive oil to the bowl.

Work the mixture until well blended.

Season the mixture with salt and pepper to taste.

Pour vegetable oil into a saucepan to a depth of about 3 inches.

Place the saucepan over medium-high heat.

Shape the fish mixture into balls about 1 1/2 inches in diameter.

Test the oil by dropping in a little batter; if it sizzles immediately, the oil is ready.

Carefully drop a few balls into the hot oil, being careful not to overcrowd the pan.

Fry the fritters until golden brown, about 2 minutes per batch.

Remove the fried fritters and drain them on paper towels.

Repeat with the remaining batter.

Serve the Bolinho de Bacalhau hot.