In a small saucepan, combine the bread flour and water and whisk to remove any lumps. Cook over medium-low heat for 3-5 minutes until the roux starts to thicken and reaches 150°F/65°C, while whisking constantly. The roux should have the consistency of a curd or pudding. Remove from heat and let cool to room temperature.
For the Japanese milk bread
In the bowl of a stand mixer fitted with the hook attachment, add the warm milk (105°F-110°F), eggs, and tangzhong. Then add the bread flour, sugar, instant yeast, and salt. Do not add the softened butter yet.
Turn the mixer on medium-low and mix for 5-7 minutes until gluten develops and the dough feels elastic.
Add the butter one tablespoon at a time and mix until the butter is completely incorporated. This may take awhile for the butter, so be patient. Once the butter is incorporated, mix for another 5-7 minutes until the dough is smooth and feels elastic. Note: The dough will be a bit tacky, but should feel elastic like a rubber band which indicates good gluten structure.
Using wet hands, shape the dough into a ball and transfer to a greased bowl or container. Cover and let rise until doubled in size for 45-60 minutes, depending on how hot your house is. Be sure to keep an eye on it because it can go fast if it’s hot outside!
Meanwhile, make the black sesame paste while you wait. See recipe below.
Shaping and final proof
Preheat the oven to 350°F. Generously grease a 9”x5” loaf pan.
For black sesame babka shape: Gently deflate the dough and roll into a rectangle on a well floured surface. Spread the black sesame paste (recipe below) over the dough in a thin, even layer using an offset spatula.
Roll the dough starting from the edge of the shorter side (want to ensure it fits into the pan) and roll into a log like a cinnamon roll placing it seam side down. Cut the dough in half lengthwise to expose the center. Braid the two pieces overlapping each piece over itself and leaving the inside exposed.
Place the loaf into a greased loaf pan and let rise for another 30 minutes, ensuring that the dough does not rise above the lip of the pan. Leave about a ¼” space because the dough will rise quite high during baking.
For traditional Japanese milk bread loaf: Gently deflate the dough and divide into 4 equal portions. Shape each piece into a ball and roll them out into an oval using a rolling pin on a well floured surface. Fold the right side (lengthwise) over to the middle and then fold the left side (lengthwise) over to the middle so both sides meet but are not overlapped. Roll the dough out into an oval again and then spread with black sesame paste. Starting from the edge of the short side, roll the dough up into a cylinder like you would roll up a sleeping bag.
Place each piece seam side down in the prepared loaf pan and repeat with the remaining dough. Cover and let rise for another 30 minutes, ensuring that the dough does not rise above the lip of the pan. Leave about a ¼” space because the dough will rise quite high during baking.
Bake the Japanese milk bread
In a small bowl, whisk together 1 egg with 1 tablespoon of whole milk or water to make an egg wash. Once the dough has proofed, brush the top of the loaf with egg wash (do not need to brush the top of the babka).
Bake for 20-25 minutes on the lower shelf until an instant-read thermometer reads 200°F when inserted into the center. If the loaf is browning too quickly, cover the top during the last 5-7 minutes with foil.
Let rest in pan 15 minutes. Remove and let cool on a wire cooling rack.
For the black sesame paste
Finely grind the black sesame seeds in a spice grinder or small food processor. Add the sugar and softened butter. Pulse to make a paste. Transfer to a small bowl, cover, and set aside.
You can refrigerate this in advance. Before using, bring to room temperature to ensure it has a spreadable consistency.