Preheat oven to 350°F . Pour oil into a 10-inch cast-iron frying pan; place pan in oven to heat the oil (the oil should be very hot when added to the potatoes).

Grate: Meanwhile, grate potatoes and onions together. (This can be done in a food processor. I favor a fine shredding blade for this.) Drain and squeeze out any residual liquid that gathers on the bottom. If using food processor, transfer potatoes and onions to a mixing bowl.

Mix: Remove pan from the oven and pour hot oil over the potato mixture. Return empty pan to the oven to keep hot; raise heat to 410°F . Stir the mixture to blend; mix in the eggs, salt, and pepper.

Bake: Using oven mitts, carefully remove pan from the oven and pour the potato mixture into the pan, spreading it evenly. Replace pan back in the oven, and bake for 10 minutes . Lower heat to 350°F and continue to bake for 1 hour or until top is golden brown .