FROM BON APPETIT
Preheat oven to 350°. Line a small rimmed baking sheet with foil. Wrap the apple in another piece of foil. Place unpeeled onion and apple on prepared sheet. Bake until tender, about 1 hour. Let cool completely, keeping the apple in the foil.
Unwrap apple; core, peel, and place with juices in a food processor. Peel onion; add to processor. Add 2 tsp. salt. Purée until very smooth. Transfer to a medium bowl. Season applesauce with salt. Cover; chill. DO AHEAD: Can be made 2 days ahead. Keep chilled.
Stir in cilantro before serving.
Meanwhile, mix celery root, potatoes, and salt in a large colander set over a large bowl to draw out moisture. Chill; let drain for 1 1/2 hours. Mix in mushrooms; let drain in refrigerator for 30 minutes longer.
Using your hands, squeeze excess moisture from the potato mixture. Transfer to another large bowl. Stir in the eggs and the next 4 ingredients; blend thoroughly. Cover the surface with plastic wrap and chill for at least 1 hour and up to 3 hours. (This will help bind the latkes.)
Preheat oven to 300°. Line a baking sheet with paper towels. Divide latke mixture into 16 equal portions on another baking sheet. Form each into a 1/2″-thick patty. Pour oil into a large nonstick skillet to a depth of 1/4″; heat over medium heat. Working in batches, fry latkes until cooked through and golden brown, about 5 minutes per side. Transfer to prepared sheet; keep warm in oven while frying remaining latkes.
Serve warm latkes with onion applesauce.