Step 1

Mix the dry ingredients. In the bowl of a stand mixer fitted with the dough hook, combine the flours, sugar, yeast, and salt. Knead on low to combine, about 30 seconds. Press a tall glass into the center of the dry ingredients to make a well.

Step 2

Add the wet ingredients. Pour the milk, eggs, butter, and vanilla into the dry ingredients and mix with a rubber spatula until a rough, shaggy dough forms.

Step 3

Knead the dough. Use the mixer to knead on medium-low for 10 minutes, or until smooth and elastic, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary.

Step 4

Proof the dough. Tip the dough out onto a lightly floured counter. Dust your hands with flour and knead the dough once or twice into a rough ball. Scrape down the bottom and sides of the bowl to remove any excess dough.Spray the bowl with cooking spray and place the dough back in the bowl. Cover with plastic wrap and let rise for 1 hour at room temprature before refrigerating overnight.

Step 5

Prep the dough and pans. Uncover the dough and discard the plastic wrap. Tip it onto a lightly floured counter. Spray two 9 x 5-inch loaf pans with cooking spray and line with parchment paper, leaving a 2-inch overhang on the long sides. Spray the parchment, too.

Step 6

Roll out the dough. Use a rolling pin to roll the dough into a large rectangle about 10 inches wide and 24 inches long. Press a bench scraper against the sides of the dough to create straight edges.

Step 7

Fill and roll the dough. Use an offset spatula to spread the pistachio cream evenly across the dough. Sprinkle the white chocolate chips evenly on top.Starting from one of the long ends, roll the dough into an even log, like you would a burrito or when making cinnamon rolls.

Step 8

Slice the dough. Use a serrated knife to cut the log lengthwise into 2 strands, each about 12 inches long.Use the knife to slice the 2 strands in half crosswise so that you have 4 pieces with the filling exposed.

Step 9

Braid the babkas. Position the 4 pieces so that the exposed layers are facing upwards and are parallel next to each other. Take 2 of the pieces and gently press together the end of each half. Then, lift the right half over the left half. Repeat this process, but this time, lift the left half over the right to create a simple, two-pronged plait. Repeat this process until there is no longer any dough left to braid — I think I was only able to cross the dough around 3 times or so. Squeeze together the ends. Congratulations! You just braided one of the babkas.Repeat with the remaining 2 pieces to create the second babka.

Step 10

Proof the babkas. Place the braids in the prepared pans and cover the top of the pans with plastic wrap. Set the loaf pans aside in a warm, draft-free spot until the dough is very soft and jiggly to the touch, 2 to 3 hours.

Step 11

Prep the oven. About 30 minutes before baking, position a rack in the center of the oven and preheat to 350°F.

Step 12

Bake the babkas. Bake the buns for 40 to 45 minutes, or until the edges are golden brown and an instant read thermometer inserted into the center of a babka reads 190°F.

Step 13

While the babkas bake, make the simple syrup. Combine the sugar and water for the simple syrup in a small saucepan. Bring to a boil over high-heat, whisking to dissolve the sugar. Set the syrup on a wire rack to cool slightly as the babkas finish baking.

Step 14

Soak the babkas. Once the babkas are done, place on a wire rack. Immediately use a pastry brush to brush the top of the babkas with the syrup, waiting until the babka(s) absorb the syrup before using more syrup—it will seem like there's too much syrup, but it will work out, I promise!

Step 15

Serve and store. Cool the soaked babkas in their pans on the wire rack for 1 hour. Serve warm, or at room temperature. The babkas will keep at room temperature, covered loosely in plastic wrap, for up to 3 days.