Heat the milk in a small pan to boiling point and then take off the heat and steep the 4 green tea teabags in the milk for a minimum of 30 minutes, overnight if you can. While it is cooling cover with cling film (plastic wrap).
Preheat your oven to 180C / 350F / Gas mark 4 and place cupcake cases in a 12 hole muffin pan. If you are not using liners very lightly grease your muffin pan.
Remove the teabags from the milk giving them a squeeze to get all the flavour out of them.
Cream the butter and sugar together until it is light and fluffy.
Add the eggs one at a time beating between each addition.
Mix the flour, green tea powder, baking powder and salt together.
Add a 1/3 of the flour mix to the batter and mix. Then add 1/3 of the milk mix in and repeat until everything is well combined.
Spoon the batter into the cupcake tin, fill each one 2/3rds full.
Pop them in the oven for 25 minutes. Checking they are firm to the touch before removing them. Once they are baked take them out of the oven and leave them in their tins for 10 minutes.
After 10 minutes transfer them to a wire rack to fully cool down.
While they are cooling it's time to make the buttercream.
Beat the butter till it is very pale in colour and fluffy.
Add in half of the icing sugar and beat. Then add in the vanilla extract and half of the milk. Then add the rest of the icing sugar and mix in.
Then add the rest of the milk a little at a time until you have the right consistency.
Mix in the green tea powder until you have a smooth green frosting.
Pipe or spoon the frosting on top of the cupcakes, sprinkle a little green tea powder on top to finish.
If you keep these in an air tight tin they should last for 4 to 5 days.