Preheat the oven to 350°F and line a baking sheet with parchment paper.
Whisk the flour and matcha powder together in a bowl until evenly combined.
In a separate bowl, beat the softened butter and granulated sugar until light and creamy.
Add the egg and vanilla extract to the butter mixture and stir until smooth.
Gradually mix the dry ingredients into the wet ingredients to form a dough.
Scoop the dough into 12 small balls and place them on the prepared baking sheet, then flatten each slightly.
Bake for 10 to 12 minutes until the edges are set. Let the cookies cool completely on the sheet.
Stir the powdered sugar and milk together to make a smooth icing.
Place a small dot of icing on each cooled cookie and press a candy eyeball into the center. Add a thin ring of icing around each eyeball to create a goo effect.