Scrub the skins of the potatoes to remove excess dirt. Place potatoes and water in a large saucepan, add the 1 tablespoon salt and 1 tablespoon vinegar. Boil the potatoes until soft, about 30 minutes. While the potatoes are cooking, mix together the mayonnaise, eggs, and onion in a large bowl; set aside. In another bowl, combine the cucumbers, tomatoes, and vinegar; sprinkle with salt, and lomi or knead the cucumbers and tomatoes until the cucumbers start to soften and release water. Squeeze the liquid from the cucumbers and tomatoes, add it to the mayonnaise mixture together with the ham; mix well; set aside. Drain the potatoes, peel, and mash. Add the mayonnaise mixture to the potatoes while the potatoes are still warm; mix well. Season to taste with salt and pepper. Chill until ready to serve. Makes 8 servings.
Approximate Nutrient Analysis per serving (not including salt to taste):
350 calories, 20 g fat, 3.5 g saturated fat, 145 mg cholesterol, greater than 1000 mg sodium, 33 g carbohydrate, 3 g fiber, 5 g sugar, 10 g protein