1) 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.
2) Add the fruit, beating gently just to combine.
3) Cover the bowl, and let the dough/thick batter rest/rise for 60 minutes; it won't appear to do too much.
4) 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.
5) 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.
6) 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.
7) 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.
8) 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.
9) To make the icing: Mix all of the ingredients together, stirring until smooth. Drizzle over completely cool babka.
Yield: 1 loaf, 12 to 16 servings.