Grate the carrots and parsnips on the large side of a box grater.
Place the first 6 ingredients (carrots, parsnips, egg, flour, salt and greek yogurt) in a bowl and combine thoroughly.
Add a thin coating of oil in the bottom of a sauté pan over medium heat.
Using an ice cream scoop or a 2 tablespoon measure, place the mixture in the oil, and press down to form a flat circle.
Cook latkes for 2-3 minutes on each side, until golden. Remove to a paper towel-lined plate to drain.
Serve with sour cream or warm applesauce.
