Preheat oven to 325 degrees F (165 degrees C). Place a sheet of parchment paper or plastic wrap on a work surface and dust with flour. Line a baking sheet with parchment paper.
Beat butter in a bowl using an electric mixer until fluffy, about 3 minutes. Add 3/4 cup sugar and continue beating until mixture is lighter in color, about 2 minutes more.
Mix flour, green tea powder, and salt together in a separate bowl; gradually add to creamed butter mixture, beating on low speed until dough sticks together. Roll dough to 1/4-inch thickness on the floured parchment paper; cut into 2-inch cookies or bars. Roll remaining dough and cut into more cookies until all the dough is used. Refrigerate for 10 minutes.
Carefully transfer cookies to the prepared baking sheet. Sprinkle sugar over each cookie.
Bake in the preheated oven until firm and barely starting to turn golden, about 15 minutes. Cool completely.