Coffee Baba au Rhum is our shortcut revival of the original sophisticated French confection. You'll earn "ooh la las" from your luncheon or teatime crowd when your serve them servings of Coffee Baba au Rhum.
Preheat oven to 350°. Whisk together yolks and granulated sugar until mixture is thick and pale (about 2 minutes). Stir in coffee extract. Sift together flour and next 3 ingredients; gently stir into yolk mixture until just blended. Stir in butter and milk until just blended.
Whisk egg whites until stiff peaks form. Fold one-third egg whites into yolk mixture. Fold in remaining egg whites. Pour into a well-buttered 10-cup Bundt pan.
Bake at 350° for 50 minutes or until a wooden pick inserted in center comes out clean. Cool in pan on a wire rack 10 minutes. (Do not remove from pan.)
Meanwhile, bring brown sugar and brewed coffee to a boil in a medium saucepan. Reduce heat to low, and simmer, stirring occasionally, 20 minutes. Remove from heat; stir in rum. Reserve 2 cups syrup. Return pan to stove top; cook over medium-low heat, stirring occasionally, 15 minutes or until slightly thickened.
Pierce cake 10 to 15 times using a skewer. Pour reserved 2 cups thin syrup over cake. Let stand 15 minutes. Invert cake onto a serving platter. Spoon desired amount of thickened syrup over cake. Reserve remaining syrup for another use (such as topping pancakes).
*The rum is optional. Replace it with an additional 1/2 cup brewed coffee, if desired.