• Preheat the oven to 350ºF (180°C).
• Line 12 muffin cups with liners or lightly grease them.
• Whisk buckwheat flour, corn starch, baking powder, and, salt in a medium bowl.
• In a large bowl, beat softened butter, sugar, and matcha until creamy. You can use an electric mixer or a hand whisk. 
• Add the eggs and the oil and mix well.
• Add the dry ingredients along with the milk, and lemon zest, and mix until well incorporated.
• Pour the mixture into the prepared pans. Fill the muffin cups ¾ full, dividing the mixture as evenly as possible.
• Bake for 20 minutes or until a tester comes out dry.
• Let cool before removing.

For the lemon icing

• Squeeze half a lemon.
• In a medium bowl mix sugar with two tablespoons of lemon juice. Mix and add more tablespoons of juice, little by little, and integrate it until you get the desired consistency. The frosting should not be too runny.
• When the muffins are completely cold, spread the icing on the top. Finish with lemon zest.