Preheat oven to 325°F/163°C.
Line a muffin tin with 6 cupcake liners.
Sift the cake flour, baking powder and matcha powder in a large bowl. Set aside.
In a separate medium bowl, combine the melted butter, whole milk and vanilla extract. Give it a stir and set aside.
Add 2 whole eggs to a stand mixer bowl (or large mixing bowl if using hand-held electric mixer) and place over the double boiler filled with simmering hot water.
Whisk until the eggs become foamy.
Add in the granulated sugar and continue whisking until the egg mixture reaches 40°C (or hot to the touch).
Remove the egg mixture from heat and continue to whip until the egg has become light yellow/pale in colour and reaches ribbon stage (when you remove the whisk and can draw a figure "8" and it sits on top for a second before disappearing). This will take about 5-8 minutes, depending on your mixer speed.
Add the sifted cake flour mixture into the whipped egg mixture in two additions, folding it in gently with a spatula, taking care not to deflate the whipped egg too much.
Take about 1 large scoop of cake batter and add it to the melted butter mixture, stirring it in to lighten.
Pour the lightened butter mixture into the cake batter and fold to incorporate using a spatula. Again, being careful not to overwork the batter.
Transfer the cake batter into the prepared cupcake liners.
Give the pan a few taps to release any trapped air bubbles.
Bake the cupcakes at 325°F/163°C for 18-20 minutes, or until a toothpick inserted comes out clean or with the slightest crumbs clinging to it.
Halfway through the bake time, or when the tops of the cupcakes have set, cover with a large piece of aluminum foil.
Remove from oven and let cool on a wire rack before frosting.