Add the flour, granulated sugar, yeast, and salt to the bowl of an electric stand mixer. Whisk to combine.
Add the eggs, egg yolk, milk, vanilla extract, vanilla bean paste, and orange zest to the flour mixture. Use the dough hook attachment on the stand mixer to mix on low speed until the ingredients come together and start to look like dough.
With the mixer still on low speed, add the room temperature butter 1 tablespoon at a time until it’s fully mixed in. Wait to add the next tablespoon of butter until the previous one is fully incorporated.
Once all the butter is mixed in, turn the mixer speed to medium and knead for 10 minutes.
Oil a large bowl. Use your hands to shape the dough into a ball and place it in the oiled bowl, rolling it around to coat. Cover the bowl with plastic wrap or a clean kitchen towel.
Refrigerate overnight, about 12 hours.
For the Filling:
Take the dough out of the fridge so it can come to room temperature.
Stir together the butter, powdered sugar, cocoa powder, and cardamom in a bowl until smooth.
To Assemble:
Butter the insides of 2 (9 by 5-inch) loaf pans.
Line a baking tray with parchment paper.
Flour a work surface and turn the dough out onto the floured surface. Cut the dough in half and shape each half into a ball.
Working with 1 ball at a time, roll it out on the floured surface into a rectangle about 10 inches by 14 inches. Spread half of the chocolate filling on top (leaving a border of about ½-inch all around). Sprinkle half of the chopped chocolate on top of the chocolate filling. Start with one of the 10-inch sides and roll the dough up into a log as tightly as you can. Place the log seam-side-down on the lined baking tray. Repeat this process with the other dough ball.
Place the entire baking tray with the dough logs into the freezer for 20 minutes.
Remove the dough logs from the freezer and place 1 onto a floured surface. Butter and flour a sharp knife and slice the dough log in half length-wise.
This next step of shaping the Babka determines how your final loaves will look, and there are several different ways to do it. You can start at the middle (cut sides facing up) and wrap the 2 log halves around each other, twisting them as you go. Or you can twist each log individually, and then wrap them around each other. No matter which method you choose, pinch both ends together once the logs are twisted together, and place it into the buttered loaf pan. Repeat this process with the other dough log.
Cover both loaves with buttered plastic wrap (or you can spray the plastic wrap with coconut oil spray), and let them rise at room temperature for 1 ½ to 2 hours.
For the Simple Syrup:
Combine the ingredients in a small saucepan over medium heat. Bring to a boil, swirling the pan to help the sugar dissolve, and then let it boil for 1 minute.
Remove from the heat and let the syrup cool to room temperature.
To Bake:
Preheat the oven to 350F during the last 30 minutes while the loaves are rising.
Bake the Babkas until they’re golden on the outside and reach an internal temperature of 185 to 190F, about 45 minutes. When it’s done cooking, the loaf should sound hollow when you tap on the bottom.
To Finish:
As soon as the Babkas are out of the oven, slowly pour the simple syrup evenly over both loaves. The bread should be hot and the syrup should be cooled for it to absorb properly.
Let the loaves cool for about 30 minutes in the pans, and then turn them out onto a wire rack to finish cooling completely.
Notes
Recipe Yield and Serving Size: This recipe makes 2 (9 by 5-inch) loaves of Babka. Cut each into 16 slices and 1 slice = 1 serving.
Storage: Like most fresh breads, Babka is best served on the same day it’s baked. However, if you wrap it well, it will keep for up to 3 days at room temperature.
Serving Tip: After the first day, I like to heat it briefly before eating (I will either toast it or microwave it for a few seconds).