Combine the crème fraîche, the smaller portion of parsley, the smaller portion of lemon zest, lemon juice, and a pinch of salt in a small bowl; cover and refrigerate while you prepare the roesti.

Toss the shredded potatoes and celery root with most of the salt in a colander and let them drain for 30 minutes to draw out excess moisture.

Working in batches, wrap the potato mixture in a clean dish towel and wring it tightly to squeeze out as much liquid as possible, then transfer the dry vegetables to a large bowl.

Add the remaining parsley, remaining lemon zest, cornstarch, and pepper to the bowl and toss thoroughly to combine.

Melt half the butter in a 10-inch nonstick skillet over medium-low heat. Add the potato mixture and spread it into an even layer, then cover and cook for 5 minutes to steam the interior.

Uncover and use a greased spatula to firmly press the vegetables into a compact, round cake. Cook until the bottom is deep golden brown, about 10 minutes, pressing down on the cake occasionally to keep it together.

Run the spatula around the edge of the pan and shake it to loosen the roesti, then slide it onto a large plate. Melt the remaining butter in the skillet, invert the roesti onto a second plate, and slide it carefully back into the pan, browned-side up.

Cook until the second side is well browned and the vegetables are tender, about 15 minutes, continuing to press on the cake occasionally.

Transfer the roesti to a wire rack and let it rest for 5 minutes—the rack prevents steam from softening the bottom crust. Cut into wedges and serve warm with the chilled lemon sauce.