In a small bowl sprinkle the yeast over the warm water.
Set aside for five to ten minutes to soften.
Pour in the milk and stir until well dissolved.
Beat in the eggs.
Set aside.
Place the flour into a large bowl and make a hole in the center.
Pour in the yeast mixture.
Mix together lightly until a very soft dough is formed.
Cover and let rise in a warm place until doubled in bulk.
In a separate bowl beat the butter until creamy.
Add the raisins, sugar and salt.
Blend the butter-raisin mixture into the dough.
Knead for five minutes.
Generously greased a savarin mold or individual molds and pour in the dough until half full.
Cover and place in a warm place to rise.
Bake at 425 degrees for fifteen minutes.
Reduce oven to 350 degrees and bake ten minutes more or until a tester inserted in the center comes out clean and the baba is golden brown.
Loosen the edges of the mold with a knife blade.
Place a platter over the mold and invert.
Prick the cake all over with a fork.
Prepare the syrup by combining the sugar and water in a small saucepan.
Bring to boil over high heat.
Reduce heat and stir until the sugar is dissolved.
Simmer for only six to eight minutes (220 degrees).
Stir in the rum.
Pour the hot syrup over the cake until it is all absorbed.
Serve with whipped cream and brandied fruits.