Heat oven to 375° F. Pulse together all the dry ingredients in a food processor until the tea leaves are pulverized.
Add the vanilla, 1 teaspoon water, and the butter. Pulse together until a dough is formed. Divide the dough in half. Place each half on a sheet of plastic wrap and roll into a 12-inch log, about 2 inches in diameter. Wrap and chill for 30 minutes. Slice each log into disks, 1/3 inch thick. Place on parchment- or foil-lined baking sheets, 2 inches apart. Bake until the edges are just brown, about 12 minutes. Let cool on sheets for 5 minutes, then transfer to wire racks.