I know folk rate the Zygon Invasion war speech, but that wouldn’t make my Top 3. Although The Doctor Falls wasn’t quite the best Capaldi episode (although it was definitely right up there, and the best in the series by far), I do think it had his best speech.
His second best I think came in Face The Raven (although Heaven Sent was the best single Capaldi episode, and most definitely one of the greatest pieces of TV ever made).
I also this short snippet from Thin Ice.
Props to Chakoteya.net for the scripts.