Whisk flour, tea, matcha, and salt in a small bowl. Cream butter and sugar in a mixer bowl on medium until pale and fluffy, about 3 minutes. On low, slowly mix in flour mixture until just combined.
Divide dough in half. Transfer each half to a piece of parchment paper; shape into logs 1 1/4 inches in diameter. Roll each log in parchment, pressing a ruler along edge of parchment at each turn to narrow the log and force out air. Freeze 1 hour.
Preheat oven to 350 degrees. Slice frozen logs 1/4 inch thick. Place 1 inch apart on parchment-lined baking sheets. Bake until edges turn golden, 13 to 15 minutes. Let cool on baking sheets on wire racks.