Rum-soaked cake (4)
I believe the answer is:
'rum-soaked cake' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for baba that I've seen before include "Rum fare" , "Rum-soaked sponge" , "a little one" , "infant" , "Ali . . . . and the Forty Thieves" .)