What exactly is ‘Bishul Beit Yosef L’Sefardim’? Is it a higher/stricter form of Kashrut?
There is a dispute between the Beit Yosef and Rama with regards to the prohibition of Bishul Akum, not eating foods cooked by a non Jew. The stringent opinion of the Beit Yosef is that a Jew must actually put the food on the fire to permit the food. According to the Rama it is sufficient if the Jew lights the flame without beginning the actual cooking. The standard you mention means the food is being prepared according to the stringent view.