Offer help....fast

Heres my dilemma. was working in boutiqe s&t and really didn't like the firm. After a year and a half and many applications send out, managed to get an offer from a top AM firm and while I was interested in staying in s&t, the offer was a solid firm, good position and could have good career growth. I verbally accepted the offer and a day later, resigned my firm to start a few weeks off vacation.
day before my offical offer letter arrives, i got a call from a previous BB i had applied to for an interview. My dilemma is that although i am happy to have the AM offer and think this could be a good move, my first choice would be the BB s&t. Do i take the interview, explain the fact that i just resigned bc of another offer but havent formally accepted it yet (i still havent sent back the contract as I just got it yesterday). Or do i take the first round interview under the guise that I am still working and then explain to them that i have an exploding offer only after the first interview. I fear that if I preface my first interview with an already exploding offer, they won't even consider me.