2 sticks (8 ounces)cold unsalted buttercut into small pieces
Sanding or granulated sugarfor garnish
Black sesame seedsfor garnish (optional)
Coat a 13-by-9-inch baking dish with butter and line the pan with 2 pieces of parchment paper that overhang each side of the pan by 1 inch. Combine flour, tea powder, powdered sugar, and salt in a large bowl and whisk until evenly combined. Drizzle vanilla and scatter butter pieces over flour mixture, and, using a pastry cutter, two knives, or your fingers, blend until dough just begins to come together.
Crumble dough into prepared baking dish and, using the base of a measuring cup or a glass dipped in flour, evenly press into the pan. Place dough in freezer while oven heats up.
Heat oven to 350°F and arrange a rack in the middle. Remove shortbread from freezer, sprinkle a few pinches of granulated sugar and sesame seeds (if using) on top of them, using the tip of sharp knife, gently score into serving portions.
Bake until shortbread is fully set and just starting to brown on the edges, about 45 minutes. Remove from the oven and let cool. Once cool, remove from baking dish and cut along score marks into cookies.