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Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Place everything except the fruit in a mixing bowl, and beat at medium speed until cohesive. Increase your mixer's speed to high, and beat for 2 minutes.
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Add the fruit, beating gently just to combine.
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Cover the bowl, and let the dough/thick batter rest/rise for 60 minutes; it won't appear to do too much.
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Scoop the batter into a greased 10-cup Bundt pan. Cover the pan, and let the dough rest/rise for 30 minutes, while you preheat your oven to 350°F.
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Bake the babka for 35 to 40 minutes, until an instant-read thermometer inserted into the center of the loaf reads at least 190°F.
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While the babka is baking, prepare the rum syrup. Combine all of the syrup ingredients in a small saucepan set over medium heat. Bring the mixture to a boil, and boil, swirling the liquid in the pan, until the sugar dissolves. Remove from the heat.
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Remove the babka from the oven. Poke it all over gently with a toothpick or fork, and slowly pour the syrup over the babka's surface.
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When the syrup is fully absorbed (about 20 minutes or so), carefully loosen the babka's edges, and turn it out of the pan onto a rack.
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If you choose to use the icing: Mix all of the ingredients together, stirring until smooth. Drizzle over completely cool babka.