Make the dough
Let’s start with the dough. In a large bowl or the bowl of a stand mixer, To make combine yeast, warm milk, and 2 teaspoons sugar and stir to dissolve. Wait 10 minutes; the mixture should get foamy and puff up. If it doesn’t, the milk was probably too hot, too cold, or the yeast is dead. Try again!
Then add 4 cups of flour and remaining sugar, and stir to combine. Add eggs, one at a time, and mix with the dough hook attachment just until the dough comes together; this may take a couple of minutes. You can also do this by hand with a spoon, no fancy mixer needed!
With the mixer on low, add salt, then butter, a little at a time, mixing until incorporated. Then, mix dough on medium speed or by hand for about 8–10 minutes until the dough is completely smooth, shiny, and slightly sticky. Make sure to scrape down the sides as you mix so everything gets incorporated. Add in more flour as you knead if it’s very sticky to get the perfect texture.
Coat a large bowl with oil (you can just clean out your mixer bowl and use that) and place dough inside, cover with plastic, and refrigerate for 12–24 hours, or until almost doubled in size. If you’re in a hurry, let dough rise in a warm spot for 1 1/2 – 2 hours until doubled in size.
It’s filling time
When the dough is resting or just about ready, make the carrot cake filling. In a food processor, pulse the carrots until fine and remove as much water as possible. You can add the walnuts in at this point after the carrots to incorporate them into the filling, or sprinkle them on top like I did. Then add in the sugar, flour and spices and pulse. Then add in the butter and egg white and pulse to combine. You should have a thick paste. You can make this up to three days ahead of time.
Put it all together
Divide the dough in 2 equal pieces and roll out one piece into a very thin 16 x 12-inch rectangle. You may have to let the dough come to room temperature a bit if it is hard to roll.
Spread half of the carrot cake filling over the dough, leaving a ½-inch (1 cm) border. Sprinkle with half of the walnuts. Brush the farthest 12-inch end with water to help dough stick to itself. Then roll the dough up into a tight log using the shorter side so you have a 12-inch log. Place roll on a lightly floured baking sheet and refrigerate. Repeat with other dough and refrigerate both for 30 minutes.
Grease two 9 x 5-inch (23 x 13 cm) loaf pans with oil and line the bottoms with parchment paper. (To get a piece that fits perfectly, trace the bottom of the pan on the parchment paper and then cutout. Magic!)
Cut each log in half lengthwise and lay them next to each other. Pinch the top ends together and twist, keeping the cut sides up so you can see the carrot cake awesomeness. Place the babka carefully in the prepared loaf pan. Repeat with the other loaf. Cover both with damp paper towels and let rise in a warm place another about 1 hour.
Bake!
Preheat oven to 350ºF with a rack placed in the middle.
Whisk the egg yolk with a little water and brush all over the loaves. Bake loaves for 40–50 minutes, or until a thermometer reads 190ºF, turning halfway through baking. Cover lightly with foil if the top starts to brown too much. Once your babkas are done, let them cool in pan for 15 minutes, then remove and finish cooling on a cooling rack.
Drizzle
While they are cooling, make your cream cheese cardamom drizzle by beating cream cheese and butter with a stand mixer. Carefully beat in powdered sugar and cardamom and then add in just enough milk to make it drizzly. Drizzle all over your cooled babkas and eat!
Notes
Store unglazed babkas wrapped well at room temperature for up to three days, though they are best the first day.
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