Directions

1. Pour the milk and 1/2 cup water into a small bowl and microwave for 30 seconds.
   
2. Add bread flour into the bowl of a stand mixer and add the salt and yeast on opposite sides of the bowl, then stir in each one with your finger. Keeping the salt separate from the yeast prevents it from killing the yeast. Add the paddle attachment.
   
3. Add 1/3 cup sugar, eggs and yolk, and 10 tablespoons butter to the standing mixer and mix on low speed until a dry, clumpy mixture forms. Gradually add in the warm milk and water mixture to form a soft, flexible, but not sticky dough. You may not use all the liquid. Cover the bowl and let it rest for 30 minutes.
   
4. Switch the attachment to a dough hook to knead the dough on medium-low speed until it passes the windowpane test, about 3 minutes. If it fails the test, knead for 1 minute longer and check again. Shape the dough into a ball and cover with plastic wrap. Let it prove in the fridge for at least 8 hours and up to 24 hours.
   
5. Place the bowl of chilled dough in a warm place for 1 hour. Meanwhile, prepare the filling by mixing brown sugar, flour, cinnamon, and 4 tablespoons butter in a bowl to form a smooth paste.
   
6. Punch down the dough and roll it out into a 9x24-inch rectangle. Spread the filling on the dough, leaving a border one inch all the way around. Roll the dough into a tight log like a roulade, starting from one of the long sides. Pinch the seam and ends to seal.
   
7. Use a sharp knife to cut the log in half lengthwise, then turn the two halves so the filling faces upwards. Twist the two lengths together, keeping the filling side up. Place the bread in a parchment-lined 9x5-inch loaf pan, tucking the ends under, and cover with plastic wrap. Let the loaf rise until it has crowned above the edge of the pan and slowly springs back when prodded with a fingertip, about 1 hour at room temperature.
   
8. Preheat the oven to 350°F. Bake the babka at for 50 minutes. It should be well browned and have an internal temperature of 190°F when it's done. Check it frequently and cover with foil after the first 20 minutes if it starts getting dark. Take the babka out of the oven and let it cool for 10 minutes.
   
9. Combine 1/4 cup sugar and 1/4 cup water in a small saucepan over medium heat until the sugar has dissolved. Take the babka out of the pan and place it on a wire rack. Brush the babka with all of the sugar syrup. Allow it to cool completely, about 1½-2 hours. Slice and serve.