Heat 2 cups of olive oil for frying in a deep frying pan to 350°F / 175°C. Fry 4 medium potatoes, peeled and cut into bite-size chunks, until tender but pale. Drain and chill in the fridge.
For the sauce, warm ⅓ cup of olive oil in a small saucepan over low heat. Stir in 1½ teaspoons of hot smoked paprika and 1½ teaspoons of sweet smoked paprika, then 1 tablespoon of all-purpose flour.
Gradually whisk in 1 cup of vegetable broth. Simmer, whisking, until velvety but still pourable, and season with salt.
Reheat the frying oil and fry the cold potatoes again until golden and crisp. Drain, season with salt and spoon over some of the sauce, serving the rest alongside.
