Combine the celery root and apples in a large bowl, toss with 1/2 of the apple cider vinegar and season with salt. Let it sit for about 1 hour. This will soften the celery root and apples.
Preheat a large saute pan over medium-high heat. Cut the mushrooms in half lengthwise and season with salt. When the pan is hot, coat with oil and arrange the mushrooms, cut side down, in the pan. Saute until the mushrooms are soft and golden brown. Flip the mushrooms over and repeat this process on the other side.
While the mushrooms are cooking, drain the excess liquid from the celery root and apple mixture, if there is any. Return the celery root and apples to the bowl, add the creme fraiche and horseradish and about 1/2 of the remaining vinegar and season with salt, to taste. Stir to combine. Taste and add the remaining vinegar if you like things very acidic; adjust the salt, if needed.
Divide the "slaw" between 4 serving plates. Lay 2 halves of the grilled mushrooms on top of the slaw and dress with mache and a sprinkling of onions.