Preheat an oven to 250°F. Line a baking sheet with paper towels.
Place the cauliflower in a food processor and pulse until pea-size pieces form. Transfer to a large bowl.
Peel the potatoes and grate them on the large holes of a box grater. Working in batches, place the potatoes in a clean kitchen towel, roll it up and twist to squeeze out as much moisture as possible. Add the potatoes to the bowl with the cauliflower. Peel and grate the onion. Using a towel, squeeze out the moisture and add the onion to the bowl. Add the eggs, flour, the 2 Tbs. chives, the salt and pepper and stir to mix.
In a large fry pan over medium heat, warm 1/2 inch of oil. Meanwhile, scoop out about 2 Tbs. of the potato mixture and flatten into a patty. Repeat with the remaining mixture to make 24 latkes.
Working in batches, place the latkes in the oil and press down with the back of a spatula. Cook, turning once, until the latkes are golden brown and crispy, 3 to 5 minutes per side. Using a slotted spatula, transfer the latkes to the prepared baking sheet and keep warm in the oven while cooking the remaining latkes.
Serve as soon as the last batch is cooked; latkes stay crisp only a few minutes. Transfer the latkes to individual plates and garnish with chives. Pass caramelized applesauce alongside. Makes 24 latkes.