Make the Tangzhong: Combine water, milk and flour in a medium saucepan. Whisk until combined and no lumps remain. Place saucepan over medium heat and cook mixture, whisking constantly, until it thickens, about 1-2 minutes. Set aside to cool.
Make the dough: While the Tangzhong is cooling, begin preparing the rest of the ingredients for the dough. Combine yeast, salt, sugar and flour in the bowl of a stand mixer. Whisk briefly by hand to combine.
Attach the dough hook to the mixer. Add melted and cooled butter, slightly warm milk, egg and the cooled Tangzhong (it can be slightly warm to the touch) to the dry ingredients. Mix on medium low until fully combined.
Increase mixer speed to medium and knead mixture for 3-4 minutes or until dough is slightly tacky but not sticky and clears the side of the bowl. It’s okay if it’s sticking to the bottom of the bowl slightly. If it seems too sticky, add another tablespoon of flour and mix for another 1-2 minutes. You can also mix and knead the dough by hand but it will take longer, more like 8-10 minutes.
Cover bowl with plastic wrap and allow the dough to rise for an hour or until 1 ½ or 2 times its original size. The time will largely depend on the temperature of your kitchen.
In the meantime, make the filling. Combine butter, salt, brown sugar and cinnamon in a medium bowl. Using a fork, mix ingredients together until a smooth, spreadable paste forms. In a small bowl, toss apples with flour. Set aside.
Once the dough has risen, preheat oven to 425 degrees. Line two baking sheets with parchment paper. Remove the dough from the bowl and place it onto a clean countertop. Divide into two pieces. Cover one piece of dough with plastic wrap. Roll other piece out with a rolling pin until it is in the shape of a rectangle that is about 8 x 15 inches in size. The dough should be smooth enough that you do not need to add flour during the rolling process. If yours is sticking the rolling pin, however, sprinkle a little flour over the dough as necessary to prevent this from happening.
Using an off-set spatula, spread half of the filling in a thin layer over the center third of the dough. Shingle a thin layer of apples on top of the filling (see photo).
Cover the filling by bringing each side of the dough to the center, overlapping slightly. You may need a metal dough scraper to help coax your dough from the counter top if it is sticking. Seal at the seams and the ends. Carefully transfer the strip to a prepared baking sheet (again, a metal dough scaper may be helpful here). Cover with plastic wrap and let rise for an additional 30-45 minutes. Repeat process with remaining dough.
Meanwhile, make the egg wash. Whisk egg and water together in a small bowl. Once the first strip is ready to go into the oven, remove plastic wrap and brush the surface of with the egg wash Sprinkle pearl sugar and almonds over the top.
Bake for 18-20 minutes or until golden brown. Repeat process with remaining strip. If the seam down the middle gives way and the strip open up while they are baking, not to worry. As they are cooling, gently coax them back together again. Cool slightly and serve warm or at room temperature.