My family never made this because it takes too long. We always bought it at one of the great Russian or Polish bakeries in Chicago. But I learned this one from Lydia, the breakfast chef where I worked in Rochester. I used to show up for work two hours early (at 6 am!) to bake with her in the morning while she simmered her pea soup when the chef wasn't around to see. She taught me her family recipes like Austrian Shortbread, Chicken Liver Dumplings and this Babka. She used candied fruit and raisins. You can use cinnamon, too.
Make the sponge: Combine the flour, sugar, yeast, and warm milk; then cover the bowl with plastic wrap and let sit at room temperature 1 hour.
Make the dough: In bowl of a standing mixer fitted with a whisk, mix together the sugar, vanilla, salt, egg yolks and eggs until well blended. Fit the mixer with a dough hook, add the flour and sponge, and mix until combined; then drizzle in the butter. Mix with the dough hook until incorporated.
Place it in a greased bowl, covered, and let it rest and rise until doubled in volume, about 1 1/2 hours.
Meanwhile, make the filling: Fit the mixer with the paddle attachment and mix together the almond paste, egg whites, and butter. Add the chocolate and mix until combined.
Preheat the oven to 350 degrees F.
Lightly flour a work surface, turn out the dough and punch it down to release the built up gases. Divide the dough in 1/2. Cover 1 piece with a damp towel as you roll the other
piece into a rectangle 8 by 14 inches and 1/4-inch thick. Let the dough rest while you roll the other out. Spread each with 1/2 of the filling, then roll them up jellyroll style and pinch the seams to seal them. Flatten the dough slightly with a rolling pin, then twist the dough 6 to 8 times. Allow the dough to rest a few minutes. Make spirals with the dough and place them in 2 greased 8-inch cake pans. (Alternatively, lay the dough straight out in 2 greased tube pans.) Cover each pan with a damp cloth, and let rise in a warm place until almost doubled in volume, about 30 to 60 minutes.
Bake the cakes for 45 minutes; then let cool in the pan.