In today's episode of Engines of our ingenuity Prof. John Lienhard traces the history of Doughnut. While capturing its history, he mentions our Vadai as one of the fore runners of the modern day doughnut. It had never occured to me why there is a hole in the middle of vadai or for that matter in doughnut, but today I got a reasonable answer when he explained the origin of doughnut.
A problem with those otherwise delicious cakes was that their centers were seldom fully cooked. In 1847, Gregory punched out the center of a cake. Now all the dough lay near the cooked surface, and he got a far more uniformly cooked doughnut.
That makes lot of sense. There is also mention of poori in the episode. You can hear it here .