Peel the celery root and potato, and then shred on the large holes of a box grater, trying to make as long a shred as possible. (Alternatively, you can use the shredder attachment for a food processor if you have one.) Add the shredded vegetables to a large bowl and use the smaller holes of the grater (or a fine zester) to grate in the shallot. Season with 2 teaspoons salt and a few grinds of pepper. Add the flour and toss until well mixed. Let sit for 15 minutes.
Lay out a piece of wax paper or parchment for the assembled patties. Taking 1/4 cup of the mix at a time, form into ball shapes, squeezing out excess liquid. Then press into very thin patties, roughly 3 inches wide and 1/4-inch thick, and put on the wax paper.
Heat the vegetable oil in a large nonstick skillet over medium to medium-high. Test the oil with a long strand of potato; if small bubbles form immediately around the potato, then the oil is ready.
When the oil is hot, add 4 latkes at a time. Cook until golden brown on the bottom, 3 to 4 minutes. Then carefully flip over with a slotted spatula and cook until the other side is brown and crispy, about 2 more minutes. Remove from the skillet and allow to drain on paper towels or a rack. Season with salt as you remove them from the oil. As you cook more latkes, keep the finished ones warm on a rack over a baking sheet in the oven. Serve with applesauce or sour cream.
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