The whole cigar/brick joke combo is best told in an evening of joke telling among a number of friends, with as much time as possible between the brick part and the cigar part. It takes quite a bit of courage and style to let the first “joke” fall completely flat, as it must, and move on, resisting any attempts to explain or answer the inevitable questions.
The second part shouldn’t come until enough time has passed that the rest of the party has pretty much forgotten the weird brick joke.
The best effect is obtained by having the second part told by a different person! A friend of mine and I pulled this off one night: I told the first part, and he did the second. At the crucial moment, he stopped and I delivered the punchline. We killed!
BTW, My favorite joke that sort of answers the OP: A Freudian Slip is when you say one thing but mean your mother.
Oh. My. God. It has taken me until the above post to get it. But now that I do I think it’s hilarious! TSLK, given the restrictions of the medium I think you did a swell job.