Well, one of the developers had a dragonborn PC that carried a piece of his own shell as a memento, didn't he? That would put the kibosh on any sort of "live birth" concept.
Seriously, though, if we have to assign biology to the concept of dragonborn boobs (as opposed to saying 'the gods made all the races, and they collaborated on the standard features), couldn't it be an evolutionary adaptation to blend in better with mammalian populations? Maybe the mammals are put off by a humanoid race in whom they can't differentiate the males and females, and so the female dragonborn evolved biologically useless cosmetic features that the more dominant mammalian races would recognize as gender cues? Maybe the dragonborn's ancestors were heavily dependent on trade with humans who lived in more resource-rich areas, and so the most successful tribes were those who, through accident or intentional breeding, had gender dimorphism that was consistent with mammalian humanoids and thus were perceived as less "alien?" One might even posit that trading was a female's job within the tribe structure, explaining why the females showed the more remarkable transformation.