Where to put question mark in sentences with two statements

I'm not sure where to put the question mark here. Can anyone help please?

1. But why would anyone want to be famous? Especially since fame brings a bunch of problems. (This punctuation reflects the intended intonation)

OR

2. But why would anyone want to be famous, especially since fame brings a bunch of problems?

Thanks.

Solution 1:

"Especially since fame brings a bunch of problems" is at best a fragment: it doesn't seem like a complete sentence. I guess this is the source of the question.

As you say, the question intonation would normally be placed in the middle, with the justification for that question tacked on the end. I would probably favour mixed punctuation, which may seem — even is — antiquated, but which appears to do exactly what you want:

But why would anyone want to be famous?—especially since fame brings a bunch of problems.

This sort of "question in the middle" is not covered by Swan in Practical English Usage, nor by Burchfield in New Fowler's Modern English Usage. I prefer my suggestion to your number 1; it may be that your number 2 actually changes the emphasis of question slightly, focusing more on the problems than why anyone would want fame at all.