1. Wash, peel and grate the potatoes and onions (a box grater on the large-hole side works well). Add the salt and allow the onion-potato mixture to drain in a colander for 10 minutes. Place the mixture in a clean dish towel and wring out the excess moisture.
2. Place the potato-onion mixture in a large mixing bowl. Add the eggs, flour, green onions and pepper.
3. Heat the oil in a 12-inch skillet over medium-high heat until it is hot but not smoking. Form the latkes by packing a one-fourth-cup dry measuring cup with the mixture.
4. Place the latkes in the skillet and flatten slightly with a spatula. Cook until they're golden brown underneath, about 3 to 5 minutes, then turn and cook the other side to golden brown. To keep the oil hot, cook only 4 to 5 at a time.
5. As the latkes finish cooking, remove them with tongs and let the excess oil drip off. Place them on a plate lined with paper towels and keep them warm in the oven. Serve with apple chutney.