A tangle of paper-thin raw fennel and cremini mushrooms tossed with olive oil, lemon and shaved Parmesan cheese makes a cool and elegant salad. You can prepare the fennel, mushrooms and cheese a few hours ahead of time and refrigerate, covered, but don't dress the salad until you are ready to serve it-it gets softer as it sits, and you want the vegetables to retain some bite.
Use a fork to whisk the lemon juice and olive oil in a small bowl. Using a mandoline or sharp knife, slice the mushrooms very thin. Put them in a serving bowl and toss with about 2 teaspoons of the olive oil mixture.
Chop enough of the fennel fronds to make about 2 tablespoons (reserve the rest for another use). Trim the tops and bottoms from the fennel bulbs and halve the bulbs; slice off most of the core (leaving on a bit helps keep the bulb intact). Using the mandoline, shave the fennel bulbs almost paper thin from the root to the top end right over the mushrooms. Add the fennel fronds and the lemon zest; season with salt and pepper. Toss to combine.
Shave the Parmesan over the salad using a vegetable peeler. Drizzle the remaining olive oil mixture around the edge of the bowl and toss everything gently but well to combine.