In a large bowl, whisk together the flour, sugar, yeast, and salt.

Gradually add the warm milk to the dry ingredients, mixing until a shaggy dough forms.

Turn the dough out onto a lightly floured surface and knead for about 5-7 minutes, until it becomes smooth and elastic.

Place the dough in a lightly oiled bowl, cover it with plastic wrap, and let it rise in a warm place for about 1 hour, or until doubled in size.

While the dough is rising, place the cold butter between two sheets of parchment paper. Use a rolling pin to pound and shape it into a 6-inch square. Keep it chilled.

Divide your risen dough in half. Take one half and set it aside. Gently knead the matcha powder into the other half of the dough until it is evenly distributed and the dough is a uniform green color.

Roll the plain dough out to about double butter block size rectangle.

Place the butter block in the center of the plain dough. Fold the dough over the butter, like an envelope, sealing the edges completely.

Gently roll the dough into a rectangle about 1/2 inch thick. Fold it into thirds, like a letter. This is your first "turn."

Wrap the dough in plastic wrap and chill in the refrigerator for 30 minutes.

Repeat the rolling and folding process (steps 9 and 10) two more times, chilling the dough for 30 minutes between each turn.

Roll the matcha dough out to about double butter block size rectangle.

Place the plain dough to the center of the matcha dough. Repeat the rolling and folding, chilling process (steps 9,10 and 11)

After the third turn, chill the dough for at least 2 hours, or preferably overnight.

Roll out the chilled dough to about 1/8 inch thickness. Cut the dough into long triangles.

Starting at the base of each triangle, gently roll it up towards the tip. Place the croissants on a baking sheet lined with parchment paper.

Cover the shaped croissants loosely with plastic wrap and let them proof in a warm place for about 1-2 hours, or until they are puffy and almost doubled in size.

Whisk together the egg and water for egg wash.

Preheat your oven to 375°F (190°C). Gently brush the proofed croissants with the egg wash.

Bake for 18-20 minutes, or until the croissants are golden brown and cooked through.

Let the croissants cool on a wire rack for a few minutes before serving.