Recipe video (my You Tube channel)https://youtu.be/GFwl0A7_rS8
For Puff Pastry DoughDice unsalted butter into about 1cm (0.4 in) cubes. Put the butter cubes in a large bowl. Put cake flour, bread flour and salt in a bowl together. Pour 90g water into a small bowl. Chill the all ingredients in a fridge 30 min.
(30 min later) Mix the flours until combined. Add the flours to the butter and toss to coat. Mix it while cutting the butter. Mix it until it becomes yellowish. If the butter seems to melt, please chill it in a fridge.
Pour the well chilled water over the dough evenly. Fold it roughly. Gather the dough.
Knead it lightly until you have a firm, rough dough. Flatten it and wrap in plastic wrap. Chill it for 2-3 hour in a fridge.
For Apple Pie FillingPeel the apples, then core. Divide each apple into 8 equally. Cut each piece in half. Put apples in a large pot.
Add lemon juice and toss apples with the lemon juice. Add granulated sugar and toss apples with the sugar. Let it sit as it is for 30 minutes.
(30 min later) Add honey and unsalted butter. Cook on medium heat. Mix it sometimes to prevent from scorching.
Put cornstarch, water and rum in a small bowl and stir it; set aside.
Turn off the heat when the sauce has reduced. Stir cornstarch mixture again and pour it over the apples. Cook until it has thickened. Add cinnamon and mix. Transfer it a container and let it cool.
Fold the puff pastry dough.Take the dough out of the fridge. Roll out it and shape into a long rectangle, sprinkling bread flour on the dough as needed. Fold the dough into thirds, like you're folding a letter.
Rotate it 90 degrees. Roll it out and fold into thirds again. Chill it in a fridge for 30 min. Repeat this whole process (roll, fold,roll, fold, chill) two more times.
Assemble and bake pie. Preheat an oven to 220 / 428 F. Divide the dough into two pieces, one about twice as large as the other. The larger piece will be the bottom and braid pastry; the smaller piece, the top. Let the smaller piece sit in a fridge. Roll out the larger piece into 3 mm (0.1 in) thick.
Wind the pastry around the rolling pin and lift it. Line a pan with the pastry.
Trim the extra pastry from the edges. Press the laid pastry against the pan. Let it sit in a freezer.
Roll out the remain pastry (the trimed edge pastry) to a 356 cm (14''2.4'') rectangle. Cut it into 6 long, thin strips. (width 1cm, 0.4 in)
Take 3 strips and braid them. Stick the other 3 strips with a little water and continue to braid. Set aside.
Put the apple filling into the pastry-lined pan. Roll out the smaller piece of dough into 3 mm (0.1 in) thick. Place it over the filling.
Cut extra pastry. Prick holes in 15 places with a fork. Brush inside of edge with egg yolk and water mixture.
Place the braid there while pressing gently. Brush whole surface with egg yolk and water mixture. Bake it at 200 / 392 F for 45-50 min.
It's all done!
