Place matcha powder in a bowl and slowly add boiling water while whisking continuously until tea is frothy and matcha is fully incorporated. Refrigerate or set aside to cool.
Mix milk, melted butter, and vanilla extract together in a large mixing bowl. Beat egg into the wet ingredients.
Mix flour, sugar, salt, and baking soda together in a bowl. Sift into another bowl.
Whisk cooled tea mixture into the milk mixture. Add sifted flour mixture to the milk mixture and mix batter thoroughly.
Heat a lightly buttered frying pan or griddle over medium heat, but do not let it smoke. Pour 1/4 cup batter into the pan and cook until small bubbles are visible near the center of the pancake, 1 to 3 minutes. Flip and cook on the second side 1 to 3 minutes more.