Preheat barbecue or grill.
Coat peppers with 3 tablespoons virgin oil and place on hottest part of grill. Cook until skins have blackened, turning regularly, about 10 minutes. Remove and allow to cool.
Cut endives in half and toss with remaining virgin oil. Place on grill and cook until soft, about 6 to 8 minutes.
Peel peppers in cool water bath. Remove stems and seeds and cut into funny shapes. Remove endives from grill and arrange capriciously with roasted peppers. Shave Provatura cheese over peppers and endive and drizzle with extra virgin olive oil. Sprinkle with lemon zest, spritz with juice and top with fresh cracked pepper.