Combine the starter and milk in the bowl of a stand mixer with the paddle attached. Or use a large mixing bowl with use a hand mixer or wooden spoon.

With the mixer running on low add 1 cup of the flour and mix until it forms a shaggy dough. Cover the bowl and set it aside for 30-60 minutes.

With the mixer running on low add the sugar, eggs and salt. Add the remaining flour and mix until the flour is incorporated.

With the mixer running, toss in the softened butter, a tablespoon at a time. Mix until the butter is incorporated. The texture will be a very thick batter or very loose dough. It will not come together like a bread dough.

Cover the bowl and set it aside at room temperature. After 30 minutes uncover the bowl, use a plastic bowl scraper to lift one side of the dough over into the middle of the dough. Repeat with the other three sides of the dough. Cover the bowl and after 30 minutes repeat the procedure. Cover the bowl and after 60 minutes repeat the procedure. Cover the bowl and after 60 minutes repeat the procedure one last time. By now the dough should be lively and airy. If the dough is still sluggish give it another hour or two at room temperature. Refrigerate over night. Meanwhile, soak the raisins in the rum.

The next day, generously butter 12 baba molds and set them onto a sheet pan. (If you're using a non-stick pan you don't need to butter.) Drain the raisins and reserve the rum. Remove the dough from the refrigerator. Stir the raisins into the dough until they are evenly distributed. Divide the dough among the prepared molds, filling each no more than 1/2 way. Cover the tray and set it aside until the dough rises to fill the molds, about 1 1/2 hours. Meanwhile, preheat the oven to 375°F.

Slide the tray into the oven and bake until well browned, about 25 minutes. Remove the tray from the oven. Turn the babas out of the pans onto a wire rack.

While the babas bake, make the rum syrup. Combine the water with the sugar in a medium sauce pan. Scrape the seeds from the vanilla bean and stir them into the syrup. Toss in the vanilla pod. Bring the mixture up to a boil. Turn off the heat. Add enough new rum to the reserved rum to bring it back up to a 1/2 cup. Add the rum to the syrup.

Place as many babas as will fit into the pot of syrup. Leave them in the syrup for 10 minutes, flipping them around after 5 minutes to soak the other side. Lift the babas out of the syrup and set them onto a wire rack set over a clean sheet pan to drain. Continue with the remaining babas. Reserve any left over syrup for plating.

Warm the apricot preserves and strain to remove the chunks of fruit. Brush the tops and sides of each baba with the preserves. Let the babas cool completely before plating and serving.

To serve. Whip the cream with the confectioner's sugar and vanilla. Place a baba on it's side on a dessert plate. Split it lengthwise and open it like a book. Drizzle the middle of the baba with left over syrup to taste. Pipe or scoop a generous dollop of whipped cream into the center.