I see what you did there!
My dictionary friend has a further observation:
‘This expression is a new way to pay a mild compliment to your interlocutor’s witticism, especially a spur of the moment witticism or one-liner. Or, posed as a question (Did you see what I did?), it is a way of highlighting that fact that you have just made a witticism — so a compliment-seeking behaviour.
Free Dictionary says it is a way to acknowledge you have ‘understood’ a joke. But, I don’t think that is right. It is more that you have ‘recognised’ that a joke was said, sometimes when no one else in the conversation has noticed the joke or has responded to it in any way.
It reminds me of I’ll pay that ... which is, of course, similar but different. Actually I’ll pay that is an expression I’ve always disliked, or at least disliked when said to me about some joke or witticism I’ve just made. I guess what I don’t like about it is that it is a begrudging recognition of one’s humour. It’s like saying, ‘well, that wasn’t funny enough to actually make me laugh, but I will admit (if I must) that it was in fact humorous and clever.’
I think that pay in this expression has the meaning ‘to give someone their due in terms of respect or appreciation’. But it isn’t a laugh. Is it a superior, more measured form of acknowledgement of shared humour, or is it, as my friend says, a grudging admission of a witticism?