To make latkes, fill a large bowl with ice and cold water. Shred potatoes using the large holes of a hand grater into the bowl of ice-cold water and let sit for 10 minutes.
Then, remove the potatoes (use tongs if necessary. The water is super cold. You may be tougher than I am) and squeeze out any extra moisture (as much as possible) into the water bowl. Finish drying potatoes really well with a towel.
Let the water sit for 15 minutes so the starch builds up on the bottom of the bowl with water. Carefully drain off water and reserve the milky white starch. You may have to scrape it off. Dry the bowl very well.
Place shredded potatoes back in the large bowl and add reserved starch. Dry again. Then add in egg, rye flour, salt and caraway seeds. If you are adding the corned beef and sauerkraut to the latkes, mix these in as well. Otherwise, save the meat for the sandwich. Or do both!
Heat up a ¼ inch layer of oil in a large sauté pan over medium heat. You know the oil is ready if a small bit of latke batter sizzles when placed in oil. Scoop ¼ cup dollops of the latke mixture into oil and flatten slightly and fry until golden brown, about 2-3 minutes. Flip and fry on the other side. Repeat with remaining batter adding more oil if necessary (make sure to heat the oil back up.)
Drain latkes briefly on towels and place on cooling racks. Season with salt immediately. Top with Russian dressing, green onions and caraway seeds! Or heat corned beef and sauerkraut in a pan and sandwich with dressing between two latkes.