With a fork, mix flour, breadcrumbs, salt, pepper, and eggs in a bowl; set aside.
Fill a large bowl with cold water. Peel half the potatoes; grate on the small, teardrop-shaped holes of a box grater, transferring potatoes to cold water as you work to prevent discoloration. Repeat with remaining potatoes, this time grating on the large, round holes.
Using a slotted spoon, transfer potatoes to a colander lined with a clean kitchen towel; add grated onion. Fold potatoes and onion in towel until as dry as possible; transfer to a large bowl.
Mix in reserved egg mixture. Form into 3- to 4-inch patties. In a medium nonstick skillet, heat 1/4 inch oil over medium-high heat until a drop of potato mixture sizzles upon contact. Reduce heat to medium. Fry latkes in batches, turning once, until deep golden brown, two to three minutes per side. Drain on paper towels; season with salt. Serve with applesauce and sour cream, as desired.