Step 1 Dissolve the yeast in the warm water and whisk in the eggs.
Step 2 Combine the flour, cocoa, sugar and salt in the bowl of a mixer. With the mixer on low speed, add the egg mixture to the dry ingredients. When the dough starts to look crumbly but has not yet come together, add the butter, a few pieces at a time. Increase the speed to medium and beat about half a minute until the butter is incorporated into the dough. This is a soft, sticky dough that will stick to the sides of the bowl.
Step 3Scrape the dough onto a lightly floured board and bring it together into a ball. Cover it loosely with plastic wrap, set it in a warm place and let it rise until doubled, 1 1/2 to 2 hours.
Step 4Grease 6 (6-ounce) ramekins with butter. Divide the dough into 6 pieces and roll each piece into a ball. Place each ball into a ramekin. Cover the ramekins with plastic wrap and let the dough rise about 45 minutes.
Step 5Heat the oven to 375 degrees. Bake the babas until the tops begin to darken, 12 to 15 minutes. Remove them from the ramekins and allow to cool completely.