I would suggest to short-circuit and make more personal what suggested in other answer. I would encourage to first reach out to the MBB people you interfaced with (both recruiting and consulting staff) during the process last year. Tell them that after a year you are still excited about the opportunity to join MBB and if it's ok for you to apply and how you should do it.
This approach will ensure that no one on recruiting side is blindsided by the fact that you are talking to people/reaching out without talking to natural contacts you built last year.
One add, in terms of expectations, after only one year no additional tenure will likely be recognized (vs what you agreed a year ago) from role you covered at another tier two consultancy.
hope it helps