Marinate mushrooms for salad: Stir together zest, lemon juice, salt, and pepper in a large bowl. Whisk in oil until combined, then stir in mushrooms and marinate while panfrying cauliflower.
Panfry cauliflower: Lightly beat eggs with salt and pepper in a medium bowl. Add cauliflower and toss until coated well. Put cheese in a large bowl. Lift cauliflower out of egg mixture with a slotted spoon and transfer to cheese, tossing to coat.
Heat oil in a 10-inch heavy skillet over moderate heat until hot but not smoking, then panfry cauliflower in 3 batches, turning occasionally, until golden on all sides, about 3 minutes per batch. Transfer with a slotted spoon to paper towels to drain.
Finish salad: Add parsley and cauliflower to mushroom mixture, tossing to combine.