Preheat oven to 400˚F (200˚C). Line two baking sheets with parchment or lightly grease.
In a medium bowl, whisk the matcha powder into the hot milk. Mix in the sweetened condensed milk.
Slowly add the flour to form a smooth, spreadable paste.
On a lightly floured surface, roll out two sheets of puff pastry until smooth and equal in size rectangles.
Spread the matcha filling into a thin layer over one of the puff pastry sheets.
Gently top with the other puff pastry sheet, pressing the edges to seal.
Cut the filled puff pastry along the short side into 15 strips about 3/4 inch (2 centimeters) wide.
Twist each strip and place on the prepared baking sheets about 2 inches (5 centimeters) apart.
In a small bowl, beat together the egg and water. Brush the egg wash over the puff pastry twists.
Bake in preheated oven until puffed and golden, about 15 minutes.
Allow to cool before topping with the icing.