UPDATE: after watching this week's episode, I see the writers are asking me to notice three other similar resonant connections:
Tyrion Lannister as the mirror of his brother. Tyrion is no warrior, yet he fought bravely defending King's Landing and nearly lost his head for it. He did not lose any body parts (in the book, he loses his nose), so he is still essentially himself--same wit and conniving. Still, like Jamie, Tyrion wants to exact revenge on those who betrayed him (Brienne makes this connection to Jamie clear in her fireside chat with him, when she tells him he must live to take revenge).
By extention, Varys' story about his castration echoes the Jamie and Tyrion theme already established. The castration may have changed who Varys thought he was, but it made him into the character he is today.
Finally, in another mirror reversal (and connection to Tyrion/Varys/Jamie), the Unsullied army rises up, all of them castrated in order to make them fierce warriors. If we see Jamie's loss of hand as a kind of castration (and the narrative is clearly asking us to), then the unsullied represent the mirror opposite of Jamie. Yet, like him, they are "prisoners," just as he was, only to be freed by a moral female leader (Danerys/Caitlyn).
Oh, and it turns out that Jamie's ploy to save Brienne from rape was a lie (not sapphires in Tarth). In that sense, he used his immoral propensity to lie to do good by the woman who was holding him captive, another ironic turn.
That makes sixteen separate ironic turns in one event.