Grate the potatoes and onion on the large holes of a box grater into a colander; add the garlic and 1 1/2 teaspoons salt and toss. Let sit 5 minutes, then wrap in a clean kitchen towel and wring out as much liquid as possible. Transfer the potato mixture to a large bowl.
Add the nutmeg, 1/2 teaspoon pepper and all but about 1 tablespoon each of the chopped celery and parsley to the bowl. Add the egg and flour and stir until combined. Form 1/4 cupfuls of the potato mixture into balls, then flatten between your palms to make thin 2-inch patties; transfer to a plate.
Preheat the oven to 325 degrees F and line a baking sheet with paper towels. Heat about 1/4 inch of peanut oil in a large nonstick skillet over medium-high heat; working in batches, add the latkes and fry until golden brown, about 5 minutes per side. Remove to the prepared baking sheet to drain, then transfer to the oven to keep warm while you cook the next batch.
Season with salt and top with the reserved celery and parsley. Serve with applesauce and/or sour cream. (The latkes can be fried up to 2 hours ahead; reheat on a paper towel-lined baking sheet at 325 degrees F, 10 to 15 minutes.)