The Minister's frustrations with the civil service continue when Sir Humphrey, at his bureaucratic best, doesn't quite deliver the policy paper the Minister is seeking.

What does the phrase in bold mean?

Thank you very much.


It is a tongue-in-cheek variation on "to be at one's best", "to be as active or intelligent as you can be:
I'm not at my best in the morning." (https://dictionary.cambridge.org/dictionary/english/best?q=best_1 ) It employs the rhetorical device known as tmesis, crowbarring an adjective in for jocular effect. Sir Humphrey is being as bureaucratic as can be.