In a bowl, combine 1 cup warm milk, yeast and 1 tsp sugar and mix together. Let sit for 10 minutes. It will start foaming and bubbling, if this doesn't happen, you will need to get new yeast as your yeast might be too old.
In a large bowl or stand mixer, add yeast mixture, eggs, remaining sugar, milk, salt, melted butter, cinnamon and matcha powder and mix.
Add 1 cup of flour at a time into mixture with your dough hook attachment in your stand mixer and add remaining flour until you create a slightly sticky bread dough. You can also mix by hand and knead the dough for about 6 minutes.
Oil your bowl and let dough rise for 1.5 hours covered in a warm place
Cut your dough into halves and divide equally into 12 dough balls
Roll each ball as round as possible and make the tops as smooth as you can and place them in a 9 inch oiled square baking dish. (The buns will be placed close together)
Cover and let rise for another 30 minutes in a warm place
Brush tops of buns with a beaten egg (be generous, you want that nice golden colour)
Preheat oven to 375F or 190C and bake buns for 15 minutes or until tops are golden brown
Let buns cool for about 15 minutes. In the meantime, combine your milk and icing sugar to create the icing. Please icing cross on top of each bun!