Trim any bad spots off the potatoes. There is no reason to peel them. Cut potatoes into chunks and place half in bowl of food processor with metal blade fitted. Add yellow onions and process till finely chopped. Dump into colander over a large bowl and allow to drain.
Change to grater blade and grate the remaining potatoes and carrots together. Add to colander and squeeze a little to remove more water. Pour the liquid off the starch in the bowl, transfer grated vegetables to bowl, and add scallions, dry ingredients and soymilk, mixing thoroughly.
Heat griddle to about 350 degrees. Oil lightly. Spoon latke mixture with a large serving spoon onto hot griddle, spreading to form cakes. Cover griddle with an inverted jelly-roll pan and allow to cook for 5 minutes. Remove pan, flip and cook for 5 minutes more, uncovered.
Hold finished latkes on platter in 275 degree oven until all have been cooked. Serve hot with soy sour cream and applesauce.