Add flour and Matcha powder to a small mixing bowl and stir together with a whisk to distribute evenly.
In the stand mixer bowl, add the egg, egg yolk, sugar, salt, vanilla extract, and beat on medium high speed until light in color and creamy.
Add the flour mixture to the egg mixture and fold with a spatula until completely combined. Add the melted and cooled butter, and fold until smooth. Refrigerate the batter for at least 1 hour before baking.
Preheat the oven to 375°F.
Brush some melted butter on each cavity of the madeleine pan and sprinkle with flour, tap the pan to cover each cavity completely with flour and shake off the excess.
Use a small ice cream scoop or tablespoon to divide the batter evenly among 12 cavities. Bake for 12 minutes.
Remove from the oven and let cool to the touch on a wire rack, flip the pan over and tap the pan until the madeleines fall out. If they don’t fall out easily, use a spatula or a butter knife to lightly pry them from the pan.
Let madeleines cool completely on the wire rack and dust with powder sugar before serving.