I think I know exactly what you mean. As Doc paraphrased, you're after quality not necessarily 'designer'. It was bound to happen eventually: I agree with you.
T-shirts, like any other product come in varying degrees of quality. The bulk of my undershirts might generously be described as semi-disposable crap. Some of my t-shirts on the other hand are, at least in my opinion crafted well with nice fabric. At the end of the day it's still a t-shirt, but not all t-shirts are the same.
I could rummage through my closet and come up with a few names, but so far I haven't found one label that consistently produces the same overall 'type'. Cuts and fabrics seem to change a lot.
So, I can't be of much help in the recommendation department but I 'get' the idea that there's a difference in quality between my undershirts, a 'beater' shirt I would wear to the gym and something well made of a higher quality fabric.
I'll hopefully be in NYC again in a month so will check out Uni Qlo again on your testimonial. I wandered through last time but didn't pick up anything.