Sprinkle the potatoes with salt and leave in a sieve for 10 minutes. Do not rinse afterwards.
Heat the olive oil in a deep-sided frying pan until quite hot, then carefully add the potatoes, in batches, and fry gently until soft but not coloured. Remove the potatoes from the pan, bring the oil back up to hot, then fry the potatoes again until crisp and deep gold. Drain on kitchen paper and keep warm.
Pour most of the oil out of the pan, then add the garlic and fry for 1 minute until softened. Add the tomatoes, chilli and paprika and cook down until reduced and sticky. Adjust the seasoning and serve alongside the hot potatoes.