The conversation in Obi-Wan’s hut probably has the most densely packed collection of these throwaway lines with canon backstories:
“[Anakin] was a navigator on a spice freighter” - The Twilight from The Clone Wars movie and a couple of episodes from the show.
“You fought in the Clone Wars?” - AotC, The Clone Wars movie and series, RotS
“For over a thousand generations the Jedi Knights were the guardians of peace and justice in the Old Republic. Before the dark times, before the Empire.” - pretty much everything before Order 66
Other throwaway lines with later explored backstories include:
“We’ll be sent to the spice mine of Kessel or smashed into who knows what!” - introduces both spice and the mines on Kessel
“We go way back, Lando and me.” - explored in Solo
Two throwaway lines that I’d like to see backstories for are:
“The bounty hunter we ran into in Ord Mantell changed my mind.”
“Many Bothans died to bring us this information” - Personally, I want this story to involve Mon Mothma having to go undercover and undergo the same type of transformative surgery that Obi-Wan underwent in the Clone Wars episode “Deception”. This would retcon how her appearance transforms from Genevieve O’Reilly in the prequels, to Caroline Blakiston in RotJ, and then back to Genevieve O’Reilly in the Ahsoka series without devaluing either actress’s performances.
[Edit: The specifics of how Obi-Wan got the nickname “Ben” would also be cool to see. We know it has to do with Satine somehow, but how did that nickname come about and why did he use it briefly in The Clone Wars series and after Order 66?]
[Edit: “I see you have constructed a new lightsaber” - How Luke got his green lightsaber is shown in a comic, but it still would be cool to see in live action or animation.]
The backstory of how Leia got the bounty hunter disguise from RotJ would also be nice to see beyond its presentation in the Forces of Destiny series.
I have the death sentence in twelve systems
As for Luke’s lightsaber, that was a deleted scene. I cannot recall if it was filmed, or just scripted.
Robot Chicken covered that one.
That’s a good one! Would have fit well for the recent Tales of the Underworld short series.
There was a brief deleted scene of Luke putting the finishing touches on the saber (canon?), but there still would be questions left with what we know now of the need for kyber crystals and each design’s connection to their constructor.