In a shallow bowl, beat the eggs with a fork. In a second bowl, mix the flour with 1/4 tsp. each salt and pepper. Using a box grater or a food processor with a shredding disk, shred the potatoes. working in four batches, wrap the potatoes in a clean kitchen towel and squeeze out as much moisture as possible; transfer to a large bowl. Season with 1 tsp. salt and 1/4 tsp. pepper.
Working with one cutlet at a time, dredge in the flour, shake off excess, dip in the egg, then press the shredded potato onto both sides of the cutlet to coat. Repeat with remaining cutlets.
In a large, heavy skillet, heat the oil over medium-high. Fry 2 cutlets, turning once, until the potatoes are crispy and brown, about 8 minutes. Drain the cutlets on paper towels and tent with foil to keep warm. Repeat with the remaining 2 cutlets.
Wipe the skillet clean and cook the bacon over high heat until crisp; transfer to a plate. Discard all but 1 tbsp. bacon fat from the skillet. Add the garlic and cook over medium-high heat, 1 minute. Add the peas and cook until hot, about 3 minutes. Roughly chop the bacon and stir it into the peas; season. Serve the cutlets with the peas and applesauce.