Serve this assortment of vegetables and nuts as a first course with French bread and butter.
Preheat oven to 350 degrees. Spread the nuts on a rimmed baking sheet. Toast until fragrant, about 10 minutes. Set aside to cool, and chop coarsely.
Place beets in a saucepan; cover with cold water. Bring to a boil; reduce to simmer. Cook until tender when pierced with the tip of a paring knife, about 30 minutes, depending on size. Drain, and rinse well with cold water. Let sit until cool enough to handle. Peel; grate beets into a bowl using large holes of box grater. Add chopped nuts; toss to combine, and set aside.
Peel and seed cucumbers. Grate on large holes of box grater, and place in a colander set over a bowl. Sprinkle with 1 teaspoon salt, and set aside for 20 minutes to let juices drain. Discard accumulated juices, transfer cucumbers to a clean kitchen towel, and wring out any additional moisture. Transfer to a bowl, and add radishes; set aside.
In another bowl, combine carrots, raisins, and parsley; set aside. Peel celery roots; grate on large holes of box grater. Place in bowl; add cornichon, capers, and chives. Add mayonnaise; stir to combine.
In another bowl, whisk together mustard and vinegar until well combined. Drizzle in olive oil, and whisk until dressing is smooth and emulsified. Season with salt and pepper; set aside.
Drizzle half of the dressing over each salad, tossing to combine. Season each with salt and pepper. Garnish beets and celery roots with additional chives, if desired. Serve at room temperature.