Preheat oven to 375°F
In a large bowl, mix the gluten-free flour, cornstarch, both sugars, tea leaves, and salt.
Add vanilla, water, and cold butter. Mix by hand or with a stand mixer until the dough comes together—it should be soft and slightly crumbly, but hold when pressed.
Divide the dough in half. Roll each half into a log about 12 inches long, wrap tightly in plastic wrap, and chill for at least 30 minutes.
Once chilled, slice into ⅓-inch rounds. Place cookies 1–2 inches apart on a greased or parchment-lined baking sheet.
Bake for 12 minutes, or until the edges are just turning golden. Let cool on the baking sheet for 5 minutes, then transfer to a wire rack to finish cooling.