- Wash celery root then set on cutting board. Cut one side of the celery root off and place cut side down on cutting board. Continue to trim away the rough edges of celery root into an approximate cube shape. Rinse cutting board and celery root again to remove any dirt or outer fibers that may cling to either. Clean up trimmed celery root with a peeler or a small knife to remove any remaining rough edges. Using a mandoline, thinly slice celery root into 1/16-inch slices. Cut lemon in half and squeeze into a bowl of water. Place celery root slices in lemon water and set aside.
- Cut the apple into quarters through the center. Place each quarter, cut side down, with the seeds facing your knife. With your blade at a 45-degree angle, slice away the seeds and core from each quarter. Run each apple quarter through the mandoline and slice into 1/16-inch slices. Place apple slices in lemon water.
- For the vinaigrette: Whisk together all ingredients except the oil. Slowly drizzle in oils, whisking quickly to emulsify.
- Remove apple and celery root from lemon water and dry. Stack a few layers of celery root and a few layers of apple on top of one another other and slice each stack into 1/16-inch-wide batons. Repeat with all celery root and apple slices. Place apple and celery root in a medium bowl. Season the mixture lightly with salt and pepper and dress with the vinaigrette. Transfer the dressed salad to a serving plate or platter and top with walnuts and watercress. Serve immediately.