Wash the potatoes and cook in boiling water for about 20 minutes, drain, quench, peel and slice. Peel onion and cut into cubes. Cut ham into cubes.
Heat the oil in a pan. Fry the diced ham until crispy and remove. Heat 1 tbsp. lard in 2 pans. Add 1/4 of each potato slices and fry for about 7 minutes, turning them until brown.
Season with salt and pepper. After about 4 minutes add 1/4 of each onion. Whisk 2 eggs twice and season with salt and pepper. Pour the eggs over the potatoes. Shortly before the mixture sticks, push them together carefully with a spatula.
Allow to set and turn out of the pan onto a plate. Keep finished omelettes warm. Prepare 2 more omelettes from the remaining ingredients as described. Wash, clean and slice the tomatoes.
Grate cheese. Wash the chives, dab dry and cut into fine rings. Cut the cucumbers lengthwise in half and slice the halves fan-like. Spread diced ham on the omelettes. Sprinkle with chives and cheese, garnish with tomatoes and cucumbers.