To make the rum syrup: In a saucepan, add water and sugar. Hold the pot handle and gently make circles to distribute sugar and water. Bring to a gentle boil and contiue simmering on low heat for10 minutes. Do not stir. (stirring can cause sugar to crystalize). Cool slightly and then stir in the rum. This is an adult dessert; the alcohol content will be present unless you cook off the alcohol in the rum. To do this, simply add the rum to the saucepan after the thread stage is reached and cook for another minute.
To make the babà dough: Mix milk, yeast and ½ cup of the flour until it forms a soft ball of dough. Cover with a kitchen towel and set aside to rise until doubled, about 30 minutes. Cut a little X in the top of the dough, which will dissapear after it has risen.
After the first rise.
Meanwhile, using a hand mixer or stand mixer, cream together sugar and butter. Stir in the whole eggs and yolk. Mix until well blended. Set aside the one egg white for another use.
Again using a hand or stand mixer, combine the little ball of yeasted dough, the egg mixture and the rest of the flour. Once a uniform dough is formed, turn out onto a floured board. Knead for 5 minutes until smooth. The kneading is important because you want to develop the gluten. If the dough gets too sticky, dust the board with a bit of flour, little by little as needed.
To prepare the babà molds: Spread a thin layer of butter around the inside and bottom of each mold and then dust with flour. You'll need a large cookie sheet to place the molds on when they go into the oven.
This dough recipe will fill twelve 3-oz babà molds. If using a scale, put 1.5 oz of dough in each prepared mold or simply fill halfway.
Cover the molds with a kitchen towel and let it rise until doubled or until the dough reaches the top of the mold. It will take about 2 hours.
Preheat oven to 350° F. Place the molds on a large cookie sheet, making sure there is at least 2 inches between each mold. If they are too close together, the centers will not cook completely.
Cook for 30 minutes until the tops are a rich dark brown.
Let the babà cool to the touch and remove from molds to cool completely. The cakes should come out very easily. If they stick a bit, you can nudge them out with a little rubber spatula.
When ready to serve, Stand the babà upright on a serving tray and drizzle the rum syrup over the top until it runs down the sides and makes a little pool on the bottom. Serve right away. Add a spoonful of fruit jam, whipped cream or a dab of Mascarpone cheese. You can make the babà cakes ahead of time and store in the fridge for a few days or in the freezer for one month. Then, when ready to serve, drizzle on the rum syrup.