Special equipment: a flour sifter or fine-mesh sieve a 12-cup Bundt pan
Sprinkle the yeast over the warm water in a large bowl. Stir a few times, then let stand until the yeast has dissolved and the mixture begins to bubble, 1 to 2 minutes. Sift 1 1/2 cups of the flour into the bowl, and stir until mostly smooth. Cover with plastic wrap, and set aside in a warm place for about 30 minutes. The mixture will expand, loosen in texture and have large bubbles on the surface.
Meanwhile, place the dried fruit, pecans, brandy and 2 tablespoons of the brown sugar in a microwave-safe bowl, stir until the sugar is dissolved, then microwave until hot and bubbling, 1 to 2 minutes. Stir, then set aside to cool.
In a medium bowl, whisk together the remaining 1 1/2 cups flour, cinnamon, cardamom and salt. Generously butter a 12-cup Bundt pan; set aside.
When the flour-yeast mixture has risen, beat the butter with the granulated sugar and remaining 3/4 cup brown sugar with an electric mixer on medium-high speed in a large bowl until light and fluffy, 3 to 4 minutes. Beat in the eggs, 1 at a time, until combined (the mixture may look slightly curdled at this stage), then add 1 teaspoon of the vanilla. Beat in the flour-yeast mixture. Reduce the mixer speed to medium-low, then gradually beat in the flour-spice mixture. Raise the mixer speed to medium, add the fruit-nut mixture with any remaining liquid and beat until the fruit is well blended. The dough should be soft, loose and elastic, almost like brioche dough or an extremely thick batter.
Transfer the dough to the prepared Bundt pan, cover with plastic wrap and let rise in a warm place until the dough fills the pan a little more than 3/4 of the way, about 1 hour. When the cake is almost done rising, preheat the oven to 375 degrees F.
Remove the plastic wrap from the cake. Bake the cake until golden brown and a cake tester comes out clean, 40 to 45 minutes. Let cool for 30 minutes in the pan on a wire rack. Loosen the sides with a small metal spatula, and turn the cake out, flat-side down, onto the wire rack to cool completely.
Before serving, stir together the confectioners' sugar, 1 tablespoon of the milk and the remaining 1/2 teaspoon vanilla in a small bowl. Gradually add as much of the second tablespoon of milk as needed to make a thick glaze that will just gently run. Spoon the glaze over the top of the cake, allowing it to run down the outside and inside.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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