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1
In the bowl of an electric mixer, whisk 2 1/2 ounces (1/2 cup) flour, the warm milk, and yeast.
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2
Cover with plastic wrap; let rise in a warm place until doubled in bulk, 1 1/2 to 2 hours.
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3
Butter twelve 3-ounce baba molds; place on a rimmed baking sheet.
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4
When flour mixture has doubled, attach bowl to mixer fitted with the paddle attachment.
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5
Add whole eggs and egg yolks, one at a time, beating on low speed until incorporated after each addition.
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6
Add the remaining 7 1/2 ounces (1 1/2 cups) flour, the granulated sugar, and the salt; beat until smooth with no lumps, about 2 minutes.
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7
With the mixer on low speed, gradually pour melted butter down the side of the bowl in a thin stream; beat until incorporated and the dough pulls away from the sides of the bowl, about 4 minutes more.
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8
Place dough in a pastry bag fitted with a 1/2-inch plain tip (such as an Ateco #806); pipe dough into prepared molds, filling each halfway.
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9
Let dough rise in a warm place until it reaches tops of molds, 30 to 40 minutes.
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10
Meanwhile, preheat the oven to 375F.
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11
If desired, toss berries with superfine sugar in a bowl; set aside to macerate.
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12
Bake, rotating sheet halfway through, until golden and a cake tester inserted in the center comes out clean, about 25 minutes.
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13
Immediately turn out baba onto a wire rack; let cool completely.
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14
Use a slotted spoon to gently drop two baba at a time into the hot Rum Syrup, submerging completely; let soak until there are no more bubbles.
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15
Place on a rack set over a rimmed baking sheet.
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16
Whisk heavy cream to soft peaks.
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17
To serve, split baba lengthwise, and top with whipped cream and berries, if desired.
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18
Combine sugar, rum, and 5 cups water in a medium saucepan.
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19
Bring to a boil over medium heat, and continue cooking until the liquid is clear, about 2 minutes.
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20
Remove from heat.
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21
Use immediately or reheat before soaking.
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22
The batter is piped into the molds until it reaches halfway up the sides.
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23
Baba are fully proofed when they rise slightly over the tops of the molds.
