The night before eating, clean the mushrooms with a damp towel peel and discard the stems (or you can use them to make stock). Grill the mushroom caps 5 to 6 minutes. Turn them, hole down, and cook another minute. Put in a bowl.
Mince 3 of the 4 garlic cloves. Zest 1 lemon and squeeze its juice. In a small saucepan, heat the oil, minced garlic, lemon juice and zest with the pepperoncini, bay leaves and thyme. Cook 5 minutes, pour over the mushrooms, and let cool in the marinade. Cover and refrigerate overnight, turning once.
To serve, grate over the zest of the remaining lemon, and the remaining garlic. Add the parsley and toss. Season with fleur de sel.