Put 1/2 cup milk and 3 green tea bags in a liquid measuring cup, cover, and refrigerate for a few hours, or overnight if possible.
Preheat the oven to 350 (F); for sea-level, preheat the oven to 325 (F).
Put the 3/4 cup plus 2 tablespoons flour*, 2 1/2 tablespoons cocoa, 3/4 cup sugar, 3/4 teaspoon baking powder*, pinch of salt, and 3 tablespoons butter in a freestanding electric mixer with a paddle attachment (or use a handheld electric whisk) and beat on slow speed until you get a sandy consistency and everything is combined.
Remove the green tea bags from the infused milk and strain into the measuring cup.
Combine the milk with 1 egg and 1/4 teaspoon vanilla; whisk the mixture together.
Slowly pour half the milk/egg/vanilla mixture, beating well until all the ingredients are well mixed. Turn the mixer up to high speed and beat to make sure there are no lumps.
Turn the mixture down to medium-slow and slowly pour in the remaining milk mixture, scraping any unmixed ingredients from the side of the bowl with a rubber spatula. Continue mixing for a couple more minutes until the batter is smooth.
Spoon the batter into paper cases lined in a muffin tin until each case is two-thirds full. Bake in the preheated oven for 20 - 25 minutes, or until the cake bounces back when touched. A skewer inserted in the center of a cupcake should come out clean.
Let the cupcakes cool slightly in the pan before turning out into a wire rack to cool completely. When the cupcakes are cold, spoon Green Tea Buttercream Frosting (recipe follows) on top and decorate accordingly.