We use celery root often in Alsace, and this salad is one of Grandma's dishes that she prepared for us in the fall, when celery roots are harvested. This fresh, crisp, light-tasting salad is very much like an American slaw. Celery root by itself is underused, but it has a wonderful flavor and texture for salads, and you can braise it by itself. It's one of those earthy vegetables, like beets, that I think people are coming back to. When shopping for celery root, choose smaller ones — the big ones can be hollow and fibrous.
Note: Though Grandma would not have done this, you can substitute lime for the lemon juice if you like.
To lighten the dressing a little, you can substitute Greek-style plain nonfat yogurt. Also, you can substitute other herbs for the chives, such as parsley, a little cilantro, basil, and nepitella (calamintha nepeta, a Tuscan favorite, in flavor a cross between mint and oregano).
Heat a small skillet over medium-low heat and add the nuts. Stir and toss until lightly toasted and fragrant, about 5 minutes. Pour onto a dish to cool, chop them coarsely, and set aside.
In a small bowl, whisk together the cream, mayonnaise, and mustard and season with salt and pepper, to taste. Set the mixture aside.
Fill a medium-sized bowl halfway with water. Squeeze the juice from 1 lemon half into the water and drop in the peel. Working as quickly as you can, peel the celery root and rub the cut edges with the second lemon half to prevent discoloration. When finished, drop this lemon half into the bowl of water, too.
Cut the celery root into several pieces and drop them into the lemon water as you go. Shred the chunks with a coarse grater or with a food processor's grating disk. You should have about 4 packed cups.
Transfer the grated celery root to a large mixing bowl, toss with the 2 tablespoons of lemon juice, and season with salt and pepper, to taste. Coarsely shred the apple and toss it with the celery root.
Add the reserved dressing, the walnuts, and half of the chives. Toss well until evenly combined. Taste and adjust the seasonings. Cover the mixture with plastic wrap and refrigerate for at least 1 hour and for up to 1-2 days.
When ready to serve, toss the salad with the remaining chives and taste for seasoning again. Add salt, pepper, and lemon juice, if needed. Arrange the salad in a serving bowl and garnish with the celery leaves.