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Preheat oven to 425°F. Line a baking sheet with parchment paper.
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Spread potatoes on the prepared baking sheet. Drizzle the potatoes with 2 tablespoons oil and sprinkle with 1/4 teaspoon salt; massage the oil into the potatoes. Roast, flipping once halfway, until golden and crispy, 40 to 45 minutes.
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Meanwhile, heat the remaining 4 tablespoons oil in a small saucepan over low heat. Increase heat to medium-high; whisk in flour, sweet paprika, hot paprika and the remaining 3/4 teaspoon salt until smooth, about 1 minute. Whisk in broth and vinegar; cook, whisking frequently, until the sauce thickens to a consistency that's good for drizzling, 4 to 5 minutes. Set aside.
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Transfer the potatoes to a serving dish. Drizzle with 2 tablespoons sauce (reserve the remaining sauce for another use) and sprinkle with parsley.