Whisk the flour, matcha, baking powder and salt in a medium bowl. Beat the butter and granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Beat in the egg and almond extract until combined. Reduce the mixer speed to low and beat in the flour mixture until just incorporated. Turn out the dough onto a large sheet of plastic wrap; shape into a disk. Wrap and refrigerate until firm, about 1 hour.
Position racks in the upper and lower thirds of the oven; preheat to 325 degrees F. Line 2 baking sheets with parchment paper. Roll out the dough until 1/4 inch thick on a lightly floured surface. Cut out cookies with a 1 1/2- to 2-inch fluted round cookie cutter or biscuit cutter. Reroll the scraps once and cut out more cookies. Arrange about 1 1/2 inches apart on the prepared baking sheets. Sprinkle generously with coarse sugar. Refrigerate until firm, about 15 minutes.
Bake, switching the pans halfway through, until the cookies are firm but not browned, 17 to 20 minutes. Let cool completely on the baking sheets.