Mix together yeast and warm milk and set aside for 5 minutes. The milk should feel comfortably warm to the touch, but not hot, otherwise it will kill your yeast.
Combine flour, egg, milk & yeast mixture, 1/2 cup of tangzhong starter in a medium mixing bowl. Mix together with your hands until combined. Cover with a damp kitchen or paper towel and let sit for 20 - 30 minutes.
Pour dough out onto clean countertop or nonstick surface. Don't worry if it is quite sticky. Gently smooth out the dough and sprinkle surface with sugar and salt. Gently fold the dough over the sugar and salt a few times. Then, mix using the fraisage method - slowly push the dough out until it is thinly smeared on the countertop, then gather back in to one lump. Repeat the smearing and gathering until you no longer feel the salt and sugar grains.
Gently smooth out the dough and place softened pieces of butter in the center. Gently fold the dough over the butter a few times. Again, mix using the fraisage method - slowly push the dough out until it is thinly smeared on the countertop, then gather back in to one lump. Repeat the smearing and gathering until you no longer see streaks of butter.
Knead using the slap and fold method. Do not add flour. Lift the dough up and "slap" it onto the countertop. Fold up, raise, and repeat until the dough is smooth and passes the window pane test. You'll notice the dough sticking more to itself than to your hands or the countertop.
Shape into a ball and place into a lightly greased mixing bowl. Cover with plastic wrap and let rise for 40 - 60 minutes until roughly doubled in size.
Remove the dough from the bowl and cut into 4 even pieces. Shape roughly until 4 balls and let rise for another 15 minutes. Lightly grease your baking tin.
Using a rolling pin, roll each ball into a rectangle about 12 inches long and 4 inches wide. Lightly flour the rolling pin to prevent sticking. With the short end facing you, roll the dough away from you to form a 4 inch wide coil. Place into the greased baking tin. Repeat with the remaining 3 balls of dough and place them side by side in the tin.
Preheat oven to 350 degrees Fahrenheit. Allow the loaf to proof for 45 - 60 minutes. When you press your finger into the loaf, it should slowly come back about halfway. Whisk together egg and milk or water, then brush the top of the loaf with egg wash.
Place in the lower third of the oven and bake for 35 minutes until golden brown and makes a hollow sound when tapped.