Using a food processor or box grater, grate parsnips and sweet potatoes.
In a large mixing bowl, combine parsnips, sweet potatoes, shallots, salt, egg whites, flour and thyme.
Heat oil in a heavy skillet over medium heat.
Working in batches, spoon 1/4 cup batter at a time on to the skillet and press down with a fork to flatten. Fry for 2-3 minutes per side, until crisp and browned. Drain on paper towels and keep warm for up to one hour in a 200F oven.