Cut fennel bulbs in quarters lengthwise, discarding outer layer if it is exceedingly tough. Use a mandoline to slice quarters thinly; slice celery equally thin.
Put sliced fennel and celery into a large bowl and drizzle with olive oil and lemon juice. Season with salt and pepper and toss gently to combine. Top with lots of freshly shaved Parmesan and chopped fennel fronds if you like.
