In a small bowl, whisk together the flour and salt.
Open up the tea bags and measure the contents to get a heaping tablespoon. Blend butter and tea together until fluffy. Add confectioners' sugar and vanilla extract. Mix on medium speed until pale and fluffy, which takes about 3 minutes. Gradually add in flour mixture until just combined.
Divide the dough in half. Form into logs about an inch in diameter (to slice) or into flat rounds (to roll out and cut with a cookie cutter). Wrap the dough in plastic wrap and freeze until firm, about 1 hour. (Or keep frozen for days or weeks, then allow to thaw in fridge for a day before proceeding with the baking.)
Preheat oven to 350 degrees. Cut the cookies into discs or with a cutter; be aware that the dough will spread when baking. Place on baking sheets lined with parchment or silicon mats.
Bake for 10 to 12 minutes, until the edges are just turning color.
OM NOM NOM!