Set a large saucepan almost filled with water to a boil. Season with salt then add the whole potatoes, and cook until tender, 25 to 30 minutes.
Drain the potatoes and set aside until cooled. Peel off the skins and mash the flesh with a fork.
In a medium skillet over medium heat, warm the olive oil. Stir in the diced onions and cook until softened, 7 to 10 minutes. Season with salt and pepper.
Add the chourico and continue cooking until the onions are caramelized, 7 to 10 minutes longer.
In a large bowl, mix together the mashed potatoes, the sautéed chourico and onions. Stir in the breadcrumbs and egg.
Shape the mixture into walnut-sized balls and chill for 30 minutes.
Fill a large pan one third full with vegetable oil and heat to 355F (180C). Fry the balls in small batches until golden brown, 2 to 3 minutes. Remove with a slotted spoon and drain on paper towels. Serve warm.