I'm not a massive bhaji aficionado - but I do have this to offer...
Where I live, there is "one" true BIR in a 50 miles radius, so when I eat out, I go there. Last Saturday I was there and ordered a chicken Vindaloo extra hot.
It was so hot I had to go for a walk to get some air. I wandered around the back of the restaurant and observed through the back door to the kitchen for a good five minutes. I saw all the usuals -- base gravy, tandoor, etc.
One thing I did definitely see was bhajis being fried to order. They had a bucket of onion/gram/spice mix and were simply forming balls and dropping them in the fryer.
Definitely no pre-cook. Their bhajis are excellent and consistent. Light outside, yet cooked through. Slightly larger than golf balls.
-- Josh