Boil the potatoes in plenty of water for about 10 minutes, until somewhat soft but not cooked through. Remove the skin and cut into cubes and dry thoroughly.
In the meantime, mash the garlic clove and mix with the lemon juice and beat in the egg yolk and salt. Mix in the olive oil a few drops at a time and beat well, but do not over beat. Continue this process with patience, until the mixture thickens and gets a rich and creamy sauce like texture.
Add in just enough oil to let the mixture emulsify, and set aside. This dish does not need a very thick aioli.
Once the aioli is done, heat the olive oil for the tomato sauce and add in the white onion and minced garlic and cook for five to seven minutes until the onion is soft and beginning to turn pale golden.
Add in the powdered cumin, smoked paprika and the tomatoes, cayenne pepper and the salt and cook for 8 minutes. Stir in the water and cook for 3 to 4 minutes and set aside.
Set the sauce aside.
Place about 2 inches of oil for frying in a skillet, and heat for about 5 minutes. Add in the cubed potatoes and fry until crisp and golden.
To serve and assemble, place a little of the tomato sauce on the plate, add the crisp potatoes over the tomato sauce.
Drizzle with the aioli and garnish with the cilantro or parsley and enjoy!