I think. The onions need to be cooked slowly until absolutely melting as we all know...Someone also mentioned soaking them in water to remove the harshness. I tried this last week and it does produce a smoother flavour. I would also only ever use Dutch onions nowadays as they attend to be milder varieties than English.
The base also needs to be very watery in my experience otherwise if it is too concentrated it can overpower the finished dish. Mix powder, garlic, ginger need to be cooked in a baghaar and added at the end for maximum flavour and an akhni stock consisting of tej patta, cloves star anise and their ilk is also a very good idea for an added dimension. (Interestingly it has been noted by top chefs that star anise and onions have an affinity with one another as the star anise helps to bring out the onions flavour!) Other than that most bases are pretty similar. Onions, peppers, tomato, carrot, fresh coriander...They all seem to be the same give or take.
Rather than people's favourite bases I think what would be interesting would be a poll of people's top techniques and tips that make a difference in producing the BIR taste.