Made from milk, curd, and sugar, mishti doi is actually a fermented dessert. Mishti doi is in fact claimed to have been a curd dip to improve gut health but because of its strong flavours, they began to sweeten it with jaggery, dates, or sugar.
But the story actually goes way back and begins with the fermented curd itself. Curd first became popular in Bulgaria. The local tribes of the region offered it to their overlords in bags that were made from animal skins. The bags in essence helped in the fermentation process. The Bulgarians have a rich history with yoghurt and their love for this has travelled in the entire continent.
With the coming of the British, came a version of the yoghurt (not to say that there is no possibility that Indians had their own curd dish) to India.
The real mishti doi was developed somewhere in the Bogra district of then Bengal and it spread like wildfire throughout the state and to other parts like Assam and Odisha. The usage of earthen pots to make the dessert is credited to the region as well. The pots let the doi thicken set while allowing the ferment to culture.
Another claim about the origins of mishti doi comes from Sherpur District, where a Bose family pioneered it. The Nawab Bogra was infatuated by the dessert and helped the family set up shop to sell this to the public.
Mishti doi is now a staple dessert in the Bengali culture and available in every sweet shop but if you want a taste of this in Delhi your best bet is CR Park.
Yoghurt companies have also tried to create their own versions but nothing is as good as the real thing.