There is more to Bombay's breads than the pao that goes into pao bhaji and vada pao. There's Brun. and there's bun. We will get there. First, you have to get to know the city's Parsis. And Iranis, who are also Zoroastrians, but came to city a little later, in the late 19th or early 20th century. And when they came, they brought with them these little cafes that dot the city.
I am no expert on Irani chai cafes. And I can't tell you whether Yazdani Bakery will provide you the best experience or Kyani's. But I can tell you a few things you need to ignore when you get there. Appearances don't matter; so ignore the fact that the marble/glass top tables and the wooden chairs look a bit dilapidated. Also ignore the rundown look the place sports.
Instead, get yourself settled. And order a bun muska. This one's familiar to you as a first cousin of the soft hamburger bun. It's similar, but just a tad bit sweeter. Maska, of course, is the generous dollop of butter that dots your bun. Now order a brun - the closest match I can think of is a crusty french roll that's soft like a cloud once you bite into it. Finally, order a chai - the sweet, milky tea that's a perfect match to both the breads.
You can get your brun fix even if you don't want to go to a cafe. Drop into City Bakery, the famous Worli landmark. Chances are you will have to jostle to get to the counter, and no one is going to let you linger. But for very few rupees, you can get your bun or brun to take home. You can also get other relatively fancy stuff, but that's not why you are here. Get brun, for that's what legends are made of.