Combine the currants and rum in a small bowl and set aside. Melt 1 tablespoon of the butter and brush a 5-cup (6 1/2 by 3 1/2-inch) tube pan or kugelhopf mold with the melted butter. Be sure to coat every crevice of the pan. Heat the milk to 115 degrees F and then pour it into the bowl of an electric mixer fitted with the paddle attachment. Stir in the yeast and sugar and allow to sit for 5 minutes.
With the mixer on low speed, first add the eggs, then the flour, salt, and remaining 4 tablespoons of butter. Raise the speed to medium-high and beat for 5 minutes. Scrape down the bowl and beater to form the dough into a ball. It will be very soft. Cover the bowl with a damp towel and allow it to rise until doubled in size, about 1 hour.
Drain the currants, fold them into the dough with a spatula, and spoon into the prepared pan. Smooth the top, cover the pan with a damp towel, and allow to rise until the dough reaches the top of the pan, 50 minutes to 1 hour.
Meanwhile, preheat the oven to 375 degrees F and make the Rum Syrup.
Bake the cake for about 30 minutes, or until a toothpick comes out clean. Allow to cool for 10 minutes, then tap it out of the cake pan onto a baking rack set over a sheet pan. Pour all of the Rum Syrup very slowly onto the warm cake, allowing it all to soak in thoroughly. Amazingly, the liquid will be absorbed into the cake, so be sure to use all of the syrup.
Heat the preserves with 1 tablespoon of water until runny, press it through a sieve, and brush it on the cake. Serve with Whipped Cream piped into the middle of the cake plus an extra bowl on the side.
Place the sugar and 1 1/2 cups water in a small saucepan and cook over high heat until the sugar dissolves. Pour into a 4-cup heat-proof measuring cup and allow to cool. Add the rum and vanilla and set aside.
Whip the cream in the bowl of an electric mixer fitted with the whisk attachment. When it starts to thicken, add the sugar and vanilla and continue to whip until the cream forms stiff peaks. Don't overbeat, or you'll end up with butter!
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