Line two large baking sheets with parchment paper. Put a master template under the parchment paper or draw about 12 1 1/2-inch circles in rows on the paper, about 1 inch apart.
Process powdered sugar, ground almond and matcha powder in a food processor until finely ground. Sift the mixture through a sieve. If there are more than 2 tablespoons of large chunks left in the sieve, grind them and sift again.
Add half of the egg whites, fold the mixture with a spatula until it becomes a thick, paste-like batter. Set aside.
Combine granulated sugar and water in a small saucepan, cook the mixture on medium high heat. When the syrup reaches 225F on a candy thermometer, start beating the other half of the egg whites on high. Continue beating while cooking the syrup until it reaches 239F. Remove from heat.
When the meringue is at soft peak stage, turn the mixer to low, and slowly pour the hot syrup into the egg whites while the mixer is running. Once all the syrup is in, turn the mixer back to high and keep whipping until the meringue is cool and glossy stiff peaks have formed.
Add about half the meringue to the almond paste, gently folding until combined and smooth. Gradually add the remaining meringue, add food color and fold until the batter is smooth. To test consistency, pick up the spatula and if the batter ribbons back into the bowl, it is ready. It should be like lava blending back into itself after about a minute.
Fit a pastry bag with a 1/2-inch round tip and fill the bag with the batter. Using the template as a guide, pipe circles onto the parchment papers.
Tap the bottom of each sheet on the work surface to release trapped air bubbles. Let the cookies stand at room temperature for at least 30 minutes. This allows the cookies to develop their crusts.
Preheat oven to 300F. Bake the macarons for 10 to 12 minutes, until set but not browned.
Transfer the baking sheets to wire racks and let the macarons to cool completely on the pans. Once cooled, gently lift half of the cookies from the parchment paper and turn them upside down.
To prepare buttercream, beat butter on high until fluffy. Add powdered sugar and matcha powder and beat until incorporated. Add milk, continue beating for another 3 minutes.
Spoon or pipe a teaspoon of buttercream onto each of the upside-down cookies. Top with the remaining cookies.
Cover and refrigerate overnight. Bring to room temperature before serving.