Toss together the sliced potatoes and 1 teaspoon salt in a medium bowl. Heat ½ cup of the olive oil in a large, heavy nonstick or well-seasoned cast-iron skillet over medium heat and add the potatoes. Cook, stirring occasionally, until the potatoes start to soften but not brown, about 5 minutes. Add the onions, peppers, sausage, and ham. Continue to cook, stirring often, until the potatoes are tender, the chorizo is cooked through, and the ingredients are well blended, another 5 to 10 minutes. Transfer the potato and onion mixture to a colander placed over a large bowl and drain. Clean the pan.
Beat the eggs in a large bowl until smooth, then stir in the potato mixture. Season with ¾ teaspoon of salt.
Return the pan to medium heat and add 2 tablespoons of olive oil. When the oil is very hot, add the egg mixture to the pan. Tilt the pan so the eggs run over the bottom of the pan in an even layer, then turn the heat to low. Cook shaking the pan from time to time, until the omelet has set, about 8 minutes.
Cover the pan with an omelet turner or flat-bottom pot lid, and flip the omelet onto the omelet turner or lid. Then carefully slide the inverted omeletback into the pan. Return to the heat and cook on the other side until lightly browned, aobut 5 minutes. Slide the omelet out onto a plate. Allow to cool to room temperature, cut into 8 wedges, and serve.