Fill a large pot 3/4 full with water.
Add a generous amount of Kosher salt, to taste.
Place over medium high heat and bring to a boil.
Add the potatoes. Boil until potatoes are tender when pierced with the tip of a knife, but not falling apart, about 10 minutes. Drain the potatoes.
Allow to cool enough to handle. Then slice into 1/4-inch thick slices.
Place a large saucepan over high heat. Add oil.
When oil is hot and shimmering, Add sliced potatoes. Cook, turning once, until golden brown on both sides. Don't turn too often, or they will start to break up. Work in batches, if you need to.
Remove browned potatoes with a slotted spoon. Set aside on paper towel-covered plates, to drain.
Discard oil and return the pan to medium heat.
Add clarified butter. When it is hot, add onions. Saute, stirring occasionally, until golden brown, about 12 minutes.
Add reserved potatoes, 1/2 teaspoon salt and pepper, to taste. Cook for 3 or 4 minutes, turning occasionally, until potatoes are crusted on the outside but still retain their shape.
Garnish with parsley and serve at once.