Dictionary:

baba

  (bä'bə)

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A leavened rum cake, usually made with raisins.

[French, from Polish, old woman.]

A French cake supposedly invented by KingStanislas I of Poland and named after Ali Baba. ‘Rum baba’ is flavoured with rum; a French modification using a ‘secret’ syrup was called brillat-savarin or savarin.

[BAH-bah] Also called baba au rhum, this rich, light currant- or raisin-studded yeast cake is soaked in a rum or kirsch syrup. It's said to have been invented in the 1600s by Polish King Lesczyinski, who soaked his stale kugelhopf in rum and named the dessert after the storybook hero Ali Baba. The classic baba is baked in a tall, cylindrical baba mold but the cake can be made in a variety of shapes, including small individual rounds. When the cake is baked in a large ring mold it's known as a savarin.

The noun has one meaning:

Meaning #1: a small cake leavened with yeast