In a bowl, combine warm milk, yeast, and a teaspoon of sugar. Let it sit for 5-10 minutes until frothy.
Add flour, remaining sugar, eggs, and salt to the bowl. Mix until a sticky dough forms.
Gradually add softened butter while kneading the dough until smooth and elastic.
Cover the dough and let it rise for about 2 hours, or until doubled in size.
Grease baba molds and divide the dough among them. Let them rise again for about 30 minutes.
Preheat the oven to 375°F (190°C) and bake the babas for 15-20 minutes, until golden.
While the babas are baking, combine prunes, Armagnac, and water in a saucepan. Simmer until prunes are plump.
Remove from heat and stir in sugar until dissolved. Let the syrup cool slightly.
Once the babas are baked, remove them from the molds and place them in a shallow dish.
Pour the Armagnac syrup over the babas, ensuring they absorb the liquid. Allow them to soak for 15 minutes before serving.