Brush the peppers with olive oil and put under the grill, turning, until blistered all over. Cover with a flded cloth and leave for 30 mins then peel of the skins. Open, deseed and cut into strips.
Mix with the next 7 ingredients, adding 4 tbsps oil and balsamic vinegar to taste. Season.
Boil or steam the broccoli flortes until just tender- usually about 3-5 mins. Drain on a cloth.
Mix the broccoli with the rest of the salad. Check seasoning and serve in a wide bowl at room temperature.