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1
Par-boil the potato cubes in well-salted water until just tender at the centre but still holding their shape — a skewer should meet slight resistance. Drain and spread on a rack. Allow to cool completely; surface moisture must be entirely absent before the first fry.
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2
Heat the frying oil to a low temperature (approximately 140–150 °C). Fry the dried potato cubes in batches until cooked through and pale gold but not yet coloured deeply. Remove and return to the rack. Cool completely; the surface will dry further and develop the microscopic fissures that create crunch surface area.
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3
Prepare the salsa brava: warm olive oil in a pan, soften the garlic without colour, add the smoked paprika and cayenne and stir for thirty seconds, then add the tomatoes. Cook to a thickened, cohesive sauce. Season with salt. The sauce must carry genuine heat — taste it; the capsaicin should be immediately present, not a background note. Keep the sauce hot until service.
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4
Raise the oil to 190 °C. This is where the dish lives or dies: the final fry must be at exactly this temperature — anything lower saturates the potato rather than crisping it. Fry the cooled potatoes in batches until the exterior is deep golden and shatters audibly when tapped with a spoon. Drain briefly, season immediately with salt.
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5
Transfer the hot potatoes to a serving vessel without delay. Spoon the hot salsa brava over liberally so that every cube is saturated — the sauce is not served alongside. In the Catalan style, place alioli separately at the table as a cooling counterpoint. Serve at once; resting causes the crust to steam and soften.