When I get a notification at the top of the screen that I've earned the Popular Question badge, I'm still not clear on how I figure out which of my questions just earned the badge.
And yes, I am looking for validation however I can get it!
Unfortunately, there's no direct way of knowing which question earned which badge.
However, you can definitely figure it out. For example: a Popular Question badge is a question with 1,000 or more views. In your profile, you can look at the questions you've asked; click the tab that says "views" to sort your questions from most views to the least; the Popular Question badge will be one that recently hit 1K views (which will be in a gold color). Although you probably won't specifically target the question the badge is referring to (unless you're keeping track of the stats of your questions which I have no idea why anyone would do), you can more or less have an idea of which question it possibly could be.