To make babas: Put the currants, cherries and apricots in a bowl with hot water and rum. Let them macerate while you prepare the dough.

In a large bowl, or in the work bowl of a heavy-duty electric mixer, sprinkle the yeast over the warm water, stirring to dissolve. Let stand for about 5 minutes. Add the flour, sugar, salt and eggs to the bowl. If using a machine, fit the bowl with the paddle attachment, and beat on a low speed. Otherwise, use a wooden spoon and beat for a minute, then turn it out onto a clean surface, and use a scrapper to gather the dough up, then slap it down, scraping and slapping to beat the soft and sticky dough. Beat the dough for about 5 minutes, stopping to scrape the sides and bottom of the bowl if you are using a machine. Take another 5 minutes to gradually beat in the soft butter, 1 piece at a time, making sure each piece is absorbed before adding the next. The dough will be very soft, but smooth and elastic.

Place in an oiled bowl at least twice the volume of the dough. Cover and let it rise at room temperate until it doubles in size. This will take about 45 minutes to 1 hour.

Brush small bucket-shaped "baba" molds of standard-size muffin tins generously with melted butter or spray with cooking spray. Preheat the oven to 350 degrees.

Deflate the dough with your fist. Drain the macerated dried fruit, reserving the liquid to add to the rum soaking syrup. Work the fruit into the dough until it is uniformly distributed. Divide the dough into 8 equal portions. Place 1 portion in each of the prepared molds or tins. Cover and let rise at room temperature until almost doubled in size. This will take about 30 to 35 minutes.

Bake until the babas are light golden brown, approximately 30 to 35 minutes. Unmold and let cool. Babas can be kept frozen for up to 2 weeks. Thaw before soaking in syrup.

To make the soaking syrup: Heat the water and sugar in a small saucepan until the sugar dissolves. Add the orange and lemon juices, rum and reserve macerating liquid. Keep warm.

To make the meringued ice cream: Line a baking sheet with parchment or waxed paper, or oil it lightly. Put the baking sheet in the freezer for a few minutes so that it is very cold. Scoop 8 portions of vanilla bean ice cream onto the prepared baking sheet, keeping the scoops at least 3 inches apart. Freeze until the ice cream is very firm.

Whisk the egg whites, sugar, water and cream of tartar in a bowl. Place over a pan of gently boiling water; the bowl should not touch the water. Cook, whisking constantly for 3 to 5 minutes, until the mixture reaches 160 degrees on an instant-read thermometer. Remove from the heat. With an electric mixer, whip until the meringue is cool and forms stiff peaks.

Put the meringue into a pastry bag fitted with a medium star tip and pipe the meringue decoratively over the frozen ice cream scoops, covering them completely. (Or, cover the frozen ice cream scoops with the meringue, lifting the meringue with the back of a spoon to create decorative swirls.) Immediately return to the freezer. Make sure the ice cream is as firm as possible before browning the meringue.

Brown the meringue with a propane torch by moving the flame back and forth about 4 inches away until the meringue is golden brown all over. You can also preheat a broiler and, watching carefully, broil until the meringue is golden brown, about 30 to 40 seconds. Immediately return to the freezer.

To assemble and serve: Cut the rounded dome off the top of each baba. Discard the dome portion. Immerse the babas, a few at a time, in the rum soaking syrup for about 1 minute, turning them so they can absorb the syrup like a sponge. Strain the leftover soaking syrup. Set it aside.

Place each baba, cut side up, on a plate. Place a meringued ice cream scoop on top of each and spoon some of the soaking syrup around. Garnish with sliced fresh fruit or berries and dried cherries, if desired.