Prepare The Babka Dough: Add the yeast into a small bowl and add 2 tablespoons of warm water to bloom and set aside for 5 minutes.
Add the flour, bloomed yeast, salt, sugar, egg yolk, and milk into a bowl of a stand mixer with the hook attachment and mix on slow speed for 5 minutes. Increase the speed and mix until it is smooth and homogenized for about 4-5 minutes.
Reduce the speed to low and add the butter in cubes, mix until the butter is combined and the babka dough is smooth with an elastic.
Place the dough in a greased bowl or container and cover it with a lid or plastic wrap. Allow the dough to bulk ferment for 2 hours. During this time the dough will develop flavor and strength.
Babka Filling: Combine the finely chopped or grated chocolate, sugar, softened butter, vanilla, and rum extract into a bowl and mix them together. Cover and set aside at room temperature.
Beat the egg with the cream until the mixture is well-mixed together, and set aside.
Line an 8X5 inch cake pan with baking paper and spray or grease with oil.
Shaping The Babka: Turn the dough over on a floured working, roll out the dough into a rectangular shape measuring 14×10 inches (35×25 cm) or 1/4 inch in thickness, and spread the filling throughout the top.
Roll the dough into a tight log shape then cut lengthwise across the middle into two even pieces, then twist together like a braid pinching each of the ends.
Place into the lined baking pan and cover with a cloth or plastic cover. If you have a proofer, you can proof at 32°C or 90°F with 80% relative humidity.
Proof the babka dough for 50 minutes or until it reaches the top of the cake pan rim.
Preheat the oven to 180°C or 355°F prior to proofing about 20 minutes before.
Once the babka cake is proofed, brush the top with the egg mixture.
Baking The Babka: Bake in the preheated oven for approximately 30-35 minutes or until golden brown on the surface.
Sugar Syrup: In the meantime, while the babka is baking, add the sugar and water to a small saucepan and bring to a boil on medium heat stirring occasionally. Keep aside.
Remove the babka cake from the oven and brush it with the sugar glaze. Allow the cake to cool in the pan for 15 minutes, then remove it and place it onto a cooling rack and cool for 30 minutes before serving.
Keep the almond chocolate babka cake wrapped in plastic wrap to retain freshness.
Enjoy!