Peel the base of the fennel bulb with a swivel vegetable peeler to remove the tougher outer layer. Slice the fennel very thinly using a sharp knife or shave on a mandoline. Add to a large platter or shallow serving bowl.
Trim off the very top and base of the celery stalks and slice in half horizontally. Lay them flat on a work surface, using a swivel peeler to make thin strips. When the stalks are too whittled down to peel, use a knife to slice the remaining stalk into 1/2-inch pieces. Add the strips and pieces to the bowl along with the red onion and mint. Tangle everything together.
To serve, top the fennel mixture with the walnuts, dates, cheese, lemon zest and a big pinch of salt. Toss gently, then add the lemon juice and a good drizzle of oil. Toss again and tasted, adding more salt, lemon juice or olive oil to taste.
To toast walnuts: Heat in a 350 degree oven on a small baking sheet or heatproof skillet for 10-12 minutes.
To prepare the salad ahead: Put the sliced fennel, celery and onion in a bowl with 1 cup ice cubes. Cover and refrigerate up to 1 day ahead. When ready to serve, drain and spin dry, add to a serving bowl and assemble with remaining ingredients.