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.
