Give user ability to add an image in a custom widget? Possible?

Hi all,
I’m developing a custom widget for a theme that I’m working on and it would really be helpful for the end user to have the ability to add an image within that widget when they’re managing it. Ideally it would function like the featured image for a post, where it could pull in a cropped thumbnail. Is it possible? My instinct would say yes, but ideally, I would be able to access the media gallery from there and I don’t know exactly how to go about that one…

And I’m aware I can add a URL anywhere and pull that in, but I was hoping for something a little easier and more intuitive, like adding an image to a post. I could also make them posts and do a custom query, but I’d rather not do that either because the content that will go down there isn’t really substantial enough to warrant it’s own post.

Does anybody have any suggestions or effective resources that they use? I’ve tried Googling a bit, but it’s kind of hard to know what to call it…