Put the potatoes in a 4-quart saucepan with the water and 1/2 teaspoon of the salt. Bring to a boil over high heat, then reduce the heat and simmer for 15 to 20 minutes, until a knife easily pierces the potatoes.

Drain the potatoes and let them cool for 30 minutes, then refrigerate them for at least 1 hour, until completely cold.

Peel the cold potatoes and cut them into 1/4-inch-thick slices.

Cook the bacon in a 12-inch skillet over medium heat for 6 to 8 minutes, stirring occasionally, until crisp. Transfer it to a plate.

Pour off all but 1 tablespoon of bacon fat from the skillet, add the onion, and cook over medium heat for 4 to 5 minutes, until softened and lightly golden; transfer it to the plate with the bacon.

Add 1 tablespoon of the oil to the skillet and arrange half the potatoes in a single layer. Cook over medium-high heat without moving them for 5 to 7 minutes, until deeply golden on the underside, then turn and cook for 4 to 5 minutes more.

Transfer the potatoes to the plate and repeat with the remaining oil and potatoes.

Return the bacon, onion, and potatoes to the skillet, add the remaining 1/2 teaspoon salt and the pepper, and toss gently over medium heat for 1 to 2 minutes, until hot. Remove from the heat and stir in the parsley.