Whisk the crème fraîche, parsley, lemon zest, and lemon juice in a small bowl. Season with salt and pepper to taste, then cover and refrigerate until serving.

Toss the shredded potatoes and celery root with the salt in a large bowl and let stand for 5 minutes to draw out moisture.

Transfer the vegetable mixture to a clean kitchen towel, gather the edges, and wring tightly to squeeze out as much liquid as possible.

Wipe out the now-empty bowl, return the dried vegetables to it, and toss with the cornstarch and pepper until the mixture is evenly coated.

Melt half of the butter in a 10-inch nonstick skillet over medium heat, swirling to coat the bottom. Add the vegetable mixture and use a spatula to press it into an even, compact layer.

Cook until the bottom is deeply golden brown and crisp, 12 to 15 minutes, shaking the pan occasionally to ensure the roesti isn't sticking.

Slide the roesti onto a large flat plate. Melt the remaining butter in the skillet, then carefully invert the roesti back into the pan, browned side up.

Continue cooking until the second side is golden brown and the vegetables are tender, 10 to 12 minutes. Slide onto a cutting board, let rest for 2 minutes, and serve hot with the crème fraîche.