Put the potatoes in a large pot and cover by 2 inches with cold water. Add 1 tablespoon of kosher salt and bring to a boil over high heat. Cook until a knife inserted into the center meets some resistance, 15 minutes. Drain and let cool slightly.
While the potatoes are cooking, heat 2 tablespoons of the oil in a large saute pan over medium heat. Add 2 tablespoons of the butter, the onions, sugar and some salt and pepper. Cook, stirring occasionally, until the onions are soft and caramelized. Remove to a platter.
Slice the potatoes in half lengthwise, then crosswise into 1/2-inch-thick half-moon-shaped slices. Sprinkle both sides of the potato slices with salt and pepper.
Heat the remaining 2 tablespoons oil in the same saute pan over medium-high heat. Add the potatoes in a single layer, then add 2 tablespoons of butter and cook on both sides (being careful not to break the slices) until lightly golden brown and crisp around the edges, about 7 minutes. Stir in the onions, remaining 2 tablespoons butter and the white wine vinegar. Finish with the parsley and thyme.
Serve hot, garnished with thyme sprigs.
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