The secret to these potatoes' creamy insides and crunchy exteriors is the pre-cooking in boiling water. Slideshow: More Portuguese Recipes
Preheat the oven to 450°F.
In a large pot of salted cold water bring the potatoes to a boil and cook until tender, 25 to 35 minutes. Drain the potatoes and let cool to warm. Peel the potatoes and cut into 1-inch pieces.
In a large cast iron skillet or oven-proof nonstick skillet, stir together the oil, paprika, and 1/2 teaspoon each salt and pepper. Stir in the potatoes until coated with the oil mixture, then roast in the oven, stirring occasionally, until very crisp, about 30 minutes. Season with salt to taste and serve.