First make a mayonnaise as the base for the remoulade. In a food processor or blender, mix the egg yolk, lemon juice, and mustard, together until smooth. With the food processor or blender running, add the oil in a very thin stream, until the oil is incorporated into the egg and the mayonnaise is thick.
Mix in the pickle relish, capers, and parsley, and season with salt, and pepper, to taste.
Peel and grate the celery root. In order to keep the grated celery root from browning, immediately stir it into the remoulade until incorporated. Cover the sauce with plastic wrap and store in the refrigerator until ready to use.
If you do not have a blender with an opening on the lid in order to add ingredients, mix by hand with either a hand mixer or whisk, adding the oil one drop at a time until you have added about 1/4 cup; then add the oil in a stream.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.