For the potato tortilla topped with cheese, peel the potatoes, slice thinly and fry slowly in a very large (wide) pan in hot olive oil over very moderate heat for about 10 minutes (or use 2 medium pans). Meanwhile, turn repeatedly with a turner.
Meanwhile, cut the onion into rings, then add and fry for another 5 minutes over not too high heat. Season with salt, pepper and oregano if desired. Beat the eggs, salt and pepper and pour over the potato tortilla. Allow to set over low heat.
Preheat the oven to 200°C.
Cut the tomatoes and cheese into small cubes and mix together. Season to taste with salt, pepper and thyme.
Sprinkle cheese and tomato cubes on top of the potato tortilla and bake briefly in the hot oven until the cheese has melted. To do this, either leave the tortilla in the (ovenproof) pan or slide it onto a baking sheet lined with baking paper. Before serving, sprinkle the potato tortilla with freshly plucked basil.