Preheat the oven to 350°F (180°C). Line 2 baking sheets with parchment paper or silicone baking mats.
In the bowl of a stand mixer fitted with the paddle attachment, lightly cream the butter on medium-high speed just until the butter is smooth, 1 to 2 minutes. Do not incorporate air into the butter. Scrape down the sides and bottom of the bowl.
Add the icing sugar, cornstarch, ground tea, and salt and mix on low speed until the dry ingredients are fully incorporated into the butter. Increase the speed to medium-high and continue to mix until smooth, 2 to 3 minutes. Add the flour and mix on low speed until most of the flour has been incorporated. Increase the speed to medium-high and continue to mix until the dough is smooth, without whipping air into the dough, 1 to 2 minutes.
Scoop thirteen 1½-tablespoon portions of cookie dough onto each prepared baking sheet, leaving ample space between them. Gently press down on the cookies to flatten them to ½-inch thickness. Using a lightly floured fork or other metal utensil, press a pattern into the tops of the cookies. Bake, one sheet at a time, for 13 to 15 minutes, or until very lightly browned around the edges. Allow the cookies to cool to room temperature on the baking sheets.
You can make these cookies ahead and store them in an airtight container at room temperature for up to 2 weeks or in the freezer for up to 2 months. Thaw the cookies, uncovered, at room temperature for 1 hour before serving.