Cut butter into cubes and place in a large bowl, cut in brown sugar and vanilla using a pastry blender. Blend until creamy.
Add matcha powder, flour and salt and continue to blend using the pastry blender. Blend until the mixture can be pressed between fingers to form a dough.
Preheat oven to 325.
Use a 1 1/2 tbsp cookie scoop to measure each cookie. Level off the scoop for uniformity then roll each scoop into a ball and place on parchment lined baking sheet.
Bake for 20-25 minutes, until the edges begin to brown. Place on a wire rack to cool.
Make the icing and frost the cookies
Pulse freeze-dried strawberries in a blender until they become dust.
Whisk together in a small bowl: freeze-dried strawberries, powdered sugar, marshmallow fluff and milk until combined. Sprinkle with salt to taste.
Once cookies are cool: scoop icing into a piping bag and trace an amoeba-shaped outline on the cookie, fill in the shape and use the piping tip to swirl and smooth the icing. Repeat this process with each cookie.