In a blender or food processor, pulse together the pistachios and Pecorino Romano until you get a fine crumble (no oil added).
Thinly slice the fennel bulb and apple. Set aside some tender fennel fronds for garnish.
Combine fennel, apple, parsley, and fennel fronds in a large mixing bowl.
Add the pistachio–cheese crumble to the salad.
Dress with fresh lemon juice, olive oil, salt, and pepper. Toss well.
Taste and adjust with more lemon or olive oil if needed.
Finish with shavings of Asiago cheese on top.
