In a saucepan, heat 3 tablespoons of olive oil over medium heat. Add the onion and garlic and sauté until the onion is soft. Turn off the heat, and add the paprika, Tabasco sauce, and thyme, stirring well. Transfer to a bowl and add the ketchup and mayonnaise. Season with salt and pepper to taste. Set aside.
For the potatoes
Bring a pan of salted water to the boil, add the cubed potatoes, bring back to the boil, then reduce the heat and simmer gently for 10 minutes or until just tender. Drain and leave to dry out in the colander. Heat 1 tbsp of olive oil in a large frying pan over a medium heat. Add the potato cubes and fry until golden and crisp - about 15 minutes.
To serve, place the potatoes in a warmed bowl and sprinkle with sea salt. Spoon over the sauce, scatter with parsley and serve.