Step 1

Prepare the Babas: Dissolve yeast in warm water in a large bowl; let stand until foamy, about 5 minutes. Whisk in eggs, butter, and sugar until smooth and completely incorporated. Fold in flour using a rubber spatula until mixture is smooth. Knead dough in bowl until it sticks to itself more than it does to your hands, about 5 minutes, dusting it with a little flour to help prevent sticking (be sure you do not use too much flour). Shape dough into a ball; place in a large bowl lightly greased with cooking spray, and dust the top with a little flour. Cover with a damp cloth, and let rise in a warm (75°F to 80°F) place until doubled in size, 1 hour to 1 hour, 30 minutes.

Step 2

Punch dough down, and knead 2 or 3 times (still in bowl). Generously coat wells of a 12-cup mini Bundt pan with cooking spray. Divide dough evenly among muffin wells (about 1 1/4 ounces each), pressing gently into bottom of each well. (You don't need to smooth the top. It will take care of itself when rising.) Let rise, uncovered, in a warm place until doubled in size, 30 to 45 minutes.

Step 3

Preheat oven to 375°F. Bake Babas in preheated oven until cakes are golden brown and spring back when lightly pressed, 12 to 15 minutes. Remove from oven; let cool on a wire rack 10 minutes.

Step 4

While Babas bake, prepare the Rum Syrup: Bring tap water and sugar to a boil in a small saucepan over medium-high. Boil mixture, stirring occasionally, until sugar is completely dissolved, about 2 minutes. Remove from heat, and stir in rum.

Step 5

Remove Babas cakes from mini Bundt pan. Pierce tops of cakes several times using a wooden pick; drizzle each cake with enough warm Syrup so that cakes are moist but not soggy (about 1 1/4 cups Syrup total).

Step 6

Place cakes on individual serving plates, and top each with 1/3 cup blackberries. Drizzle each with a little more Syrup. Garnish with fresh whipped cream. This dessert should be served warm, but both the cakes and the syrup hold well, so you can reheat both to serve them later.