In a large bowl, combine the flour, sugar, and salt. Add the cold, cubed butter and mix with a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Gradually add the cold water and matcha powder, mixing until a dough forms. Do not overmix. Wrap the dough in plastic wrap and refrigerate for at least 1 hour.
On a lightly floured surface, roll out the chilled dough into a rectangle about 1/4 inch thick. Fold the dough into thirds like a letter, then roll it out again into a rectangle. Repeat this folding and rolling process two more times to create layers.
After the final roll, cut the dough into triangles. Place a small amount of almond paste at the wide end of each triangle and roll it up tightly towards the point.
Place the rolled croissants on a baking sheet lined with parchment paper. Brush the tops with the beaten egg and sprinkle with sliced almonds.
Preheat the oven to 375°F (190°C) and let the croissants rise for 30 minutes while the oven heats.
Bake for 15-20 minutes or until golden brown. Remove from the oven and let cool slightly before dusting with powdered sugar.