2 large artichokes
2 large fennel bulbs
1/4 cup extra-virgin olive oil
1 to 2 tablespoons white truffle oil
Salt and pepper
1 piece Parmesan cheese (about 3 ounces)
About 1/2 cup Italian parsley leaves
Pare the artichokes down to their hearts and scoop out the chokes with a spoon; dropping them into water acidulated with the juice of 1 of the lemons.
Cut off the feathery tops of the fennel at the base of their stalks and remove the outer layer of the bulbs. Slice the bulbs very thin with a mandolin or a very sharp knife. Remove the artichoke hearts from the water and slice them very thin the same way.
Assemble the salad in layers on a large platter or on individual salad plates. First make a layer of the fennel slices. Squeeze lemon juice evenly over the fennel and drizzle with salt and pepper. Then make a layer of the artichoke hearts, also slice very thin. Squeeze more lemon juice over them, drizzle evenly with another third of the oils, and season with salt and pepper. Cut thin shavings of the Parmesan with cheese slicer or a vegetable peeler and arrange them on top of the artichoke slices. Scatter the parsley leaves over the cheese, season with salt and pepper, squeeze more lemon juice over, and drizzle evenly with the rest of the oils. Serve immediately.