Dissolve the yeast in 3 1/3 tablespoons of warm water, and let it double in volume.
Mix the flour with the salt, 1 teaspoon of sugar, eggs, yeast, and a little water.
Work the dough until it forms a ball. Let it rest for 30 minutes at room temperature.
Melt the butter, let it cool, and incorporate it into the dough. Work the dough again until it no longer sticks, then fill a savarin mold with it. Let it rise to the edge of the mold.
Preheat the oven to 428°F.
Bake the baba for 25 minutes. Unmold and let it cool on a rack.
Boil 1 cup of water with the sugar. Add 1/2 cup of rum. Soak the baba with this syrup and place it on a dish.
Heat the remaining rum, flambé the baba, and serve immediately with whipped cream.