I have always had Begun bhorta, but this is the first time my sister in law ( Una) made the begum bhorta with an egg (deem). It tasted really good, and the hard boiled egg gave a creamy texture that was quite unique!
Some people like to have the eggplant really burnt, others prefer it slightly burnt so that there is a little bit of burnt smell in it. Just make sure that the eggplant is soft or else it will not taste good! You can check with a butter knife if the eggplant has softened.