Whisk the crème fraîche, parsley, lemon zest, lemon juice, salt, and pepper in a small bowl until combined. Cover and refrigerate until the roesti is ready to serve.

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

Transfer the vegetables to the center of a clean kitchen towel, gather the ends, and wring the bundle vigorously over the sink until no more liquid can be squeezed out.

Return the dried vegetables to the bowl and sprinkle with cornstarch and pepper. Toss thoroughly to coat, breaking up any clumps with your fingers.

Melt half the butter in a 10-inch nonstick skillet over medium heat. Add the vegetable mixture to the pan, spreading it into an even layer and pressing down firmly with a spatula to compact the cake.

Cook the roesti until the bottom is deeply golden brown, about 10 to 12 minutes. If the edges begin to darken too quickly, reduce the heat slightly to ensure the interior cooks through.

Slide the roesti onto a large flat plate. Place the inverted skillet over the plate, then carefully flip the plate and skillet together to return the roesti to the pan, browned-side up.

Add the remaining butter to the pan, lifting the edges of the roesti to allow it to melt underneath. Cook for another 8 to 10 minutes until the second side is crisp and golden.

Slide the cake onto a cutting board and let it rest for 5 minutes. Slice into wedges and serve hot with the chilled crème fraîche.