Grate celeriac using a mandoline. Select the blade which will grate it in a thin, noodle-like shape. See the photos. Place the grated celeriac in a large bowl.
Add sliced pickled red bell peppers and fresh chopped parsley.
Make avocado mayo dressing: Add all ingredients except oil in the bowl of your food processor and blend until smooth. Drizzle the oil slowly into the processor while blending.
Add avocado mayo over the celeriac noodles in the bowl and mix.