This salad goes all-in with the mushroom flavor, while salty pecorino and crunchy celery provide balance. Tearing the shiitakes into pieces makes for easier prep, and the jagged edges get nicely brown when sautéed.
In a small bowl, whisk together 4 tbsp. oil, the vinegar, 3/4 tsp. salt, and 1/4 tsp. pepper and set aside.
Put celery leaves, celery, spinach, and parsley in a salad bowl.
Heat remaining tbsp. oil in a 12-in. frying pan over medium-high heat until shimmering. Add mushrooms and cook undisturbed until browned on underside, 1 to 2 minutes. Season with 1/4 tsp. salt and cook, stirring occasionally, until browned and tender but not too soft, 2 to 3 minutes.
Transfer mushrooms to bowl with celery, add vinaigrette and hazelnuts, and toss to coat. Scatter cheese over salad, season to taste with more salt and pepper, and toss again.