Disclaimer: as my username suggests, I'm female, but have no weird motives for posting here. I've just been reading these boards and finding them enlightening and entertaining in equal measure, so I thought I'd give something back. Hope it helps.
Sounds potentially worrying, particularly the "telling you you're bigheaded" bit. At the "almost as gorgeous as me" line, it's simply good manners to say, "Indeed, no one could hold a candle to your splendour" or "Nah, he's better looking, but I'm sure you make better cups of tea. Speaking of which..." Such a response indicates that she thinks he's better looking and you'll have to live with that, but that it's you that she's fond of. A *****y reply is Not Good. To give one in the first few weeks of going out would serve to keep you on your toes, but you're past that stage.
Of course, her professed interest in him might be totally innocuous: she might have no real designs on him or anyone else. Some girls just have *really* poor judgement about how much time they should spend thinking about other men and who they should mention it to. If this is the case, then a simple "you know what? I don't care. Now get over him, ok?" should be sufficient.
But I think you need to establish whether this is in fact the situation. You may be able to get him to stop her from talking about him, but will she stop *thinking* about him and anyone else she finds attractive? Women have crushes on other men from time to time - it can't be helped - but it's good grace to attempt to get over them ASAP, never mind relishing in them. How would she respond if he (or someone else she liked) showed an interest in her? If she wants to go out with you, she needs to indicate that she's happy to do so, and isn't going to trade you in for a better model as soon as one comes along.
As to how to deal with it? On the rare occasion that I admitted to my ex that I found a guy attractive, he'd calmly say, "Oh yes? Do you want to go out with him, then?" to which I'd answer "Nah, it wouldn't work" or "Well, in another situation, maybe, but I'm with you and that's fine with me" accordingly, and all was well. So you might want to ask that if she brings the subject up again.
A bit of "testing the water" in this respect is sensible (since some men get ridiculously jealous), such as commenting on other guys occasionally or hanging out with male friends unaccompanied. But this is taking it too far for it to be a test, unless she's trying to establish where your cut-off point is as to what you'll tolerate (but that seems unlikely). Ask what she's trying to achieve.