Heat oven to 200°F; set rack over rimmed sheet. Coarsely grate potatoes and onion; squeeze firmly in a clean towel until little liquid remains.

Mix shreds with eggs, flour, salt, and pepper just to coat evenly. Plan 16 equal portions; cook promptly.

Heat 2 tablespoons oil in a large heavy skillet over medium-high until shimmering. Add 4 spaced portions; flatten each to about 3 inches wide and 1/4 inch thick.

Cook 3 to 4 minutes per side until deeply golden and centers tender with no wet egg. Transfer to rack in warm oven.

Repeat in 3 more batches with 2 tablespoons fresh oil each, adjusting heat to prevent scorching. Serve promptly, 2 per person.