Cover a plate or cooling rack with paper towels. Then, use a box grater to grate the carrots and the parsnips. In batches, squeeze the carrot and parsnip shreds over the sink until all the liquid is removed. Set them aside in a medium mixing bowl and repeat until all the carrots and parsnips have been squeezed dry.
Add the leeks, eggs, flour, dill, garlic powder, and black pepper to the bowl and using a wooden spoon or your hands, mix until everything is well combined. Add extra flour if the batter feels too wet and runny.
In a large nonstick skillet, heat 2 tablespoons of oil. When hot and ready, carefully make small patties (about ½ cup each) from the batter and place into the skillet, working in batches to not overcrowd the pan. Fry until golden brown, about 5 minutes per side, and then transfer the latkes to the paper-towel-lined plate or cooling rack. Repeat until all the batter has been latke’d and cooked. Serve immediately with applesauce and Greek yogurt.