Shred potatoes and onion in a food processor; drain well.
Stir together biscuit mix and egg; add potato and onion.
Pour peanut oil to a depth of 1/2 inch in a large, heavy skillet. Drop potato mixture by tablespoonfuls into hot oil, and fry mixture, in batches, over medium heat 2 minutes on each side or until golden brown. Drain latkes on paper towels. Serve latkes with applesauce and sour cream, if desired.