Preheat the oven at 395°F (200℃).
Put butter in a pan, and heat it until it turns brown without burning, stirring occasionally to make browned butter. Set it aside and let it cool slightly.
Combine the cake flour, almond meal, sugar, matcha powder, and baking powder, and sift them together. Add the egg whites and mix until the batter is smooth and uniform. Then, strain the browned butter into the mixture, stirring well to combine thoroughly. Chill in the fridge for 30 minutes to an hour.
Brush melted butter (not listed in the ingredients) onto the financier or madeleine molds. Place the chilled batter in a piping bag, and fill the molds to 3/4 full.
Bake in the oven about 15 minutes or golden brown.