Cover the salt cod with cool water. Soak for 36 hours, changing the water every 8 hours.
Drain cod and pat dry. Heat 1 tablespoon olive oil in a skillet over medium heat. Add cod and cook until warmed through and softened. Cool and then shred. Set aside.
Heat remaining olive oil in a skillet set over medium heat. Add onions and saute until tender. Remove from the heat and cool.
Put egg yolks in a bowl and lightly beat. Add cooled onions, shredded cod, potatoes, salt, pepper and parsley. Mix thoroughly.
Mold into bite-sized portions in your preferred shape – typically served as a round orb or football-like with pinched edges on either side.
Heat a pot of vegetable oil to 350F. Fry bolinhos until browned and crispy.