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