Giant Stuffed Mushrooms

Name: Giant Stuffed Mushrooms
Ingredients: Extra-virgin olive oil, for liberal drizzling, plus 1/4 cup; 5 large portobello mushroom caps; 2 tablespoons finely chopped fresh rosemary leaves, a couple of sprigs; Salt and pepper; 1 cup diced, stale chewy bread; 2 plum tomatoes, chopped; 2 ribs celery from the heart with green tops, very thinly sliced; 1/2 small onion, chopped; Couple handfuls flat-leaf parsley, leaves chopped; 1 lemon, juiced; Small chunk Parmigiano-Reggiano, to shave on salad