Question on British slang

I’m watching a documentary on the Royal Scot’s (train) journey through the Peaks District. At one point, the narrator says “The service staff [cooks, waiters] continue to woo the passengers with even more [what sounded to me like] belize.” [Cut to passengers imbibing cocktails.]

What is “belize”? Or did I mishear the narrator completely?

How was it pronounced, rhyming with flies or fleas, say?

The latter, like the name of the country Belize.

I found the episode on YouTube. The line is apparently “oil the passengers with still more Belinies”:

Around the 39:00 mark.

I get it now: Belini is the name of the cocktail.

https://www.bawarchi.com/recipe/belini-ogsmvFbiajgff.html

More commonly spelled “Bellini”, like (but nothing to do with) the opera composer - apparently named after a lesser-known Venetian artist.

That tickles! :face_with_hand_over_mouth: