In a food processor, pulse together the flour, tea, lavender and salt, until the tea and lavender are just spotted throughout the flour.
Add the confectioners' sugar, vanilla and butter. Pulse together until a dough is formed. It may seem like it’s not coming together at first. Just keep pulsing and it will—but don't overdo.
VERY IMPORTANT STEP. Transfer dough to a bowl, cover with plastic wrap and put the bowl in the fridge for 1/2 hour.
After 1/2 hour, preheat the oven to 375ºF. Line two baking sheets with parchment paper or silicone baking liners.
Take dough from fridge and, using your hands, form balls of dough about 1 inch in diameter. This is where you will see the value of chilling the dough; it will form into balls easily, being quite malleable. You can pinch pieces off or add pieces on at will, and it will hold together beautifully.
Place dough balls on lined cookie sheets about 2 inches apart. Using a flat-bottomed glass, press the balls to about 1/3-inch thick. The cookie disks may stick to the bottom of the glass, but you can easily twist them off. You can also slightly reshape imperfections and fix cracks in the edge. Wiping the glass on a paper towel occasionally reduces sticking.
Bake cookies, one cookie sheet at a time, for 12 to 14 minutes. Shortbread cookies stay pretty pale, only browning slightly around the edges, so don’t overdo. Just keep an eye on the edges.
Cool cookies on cookie sheet for 5 minutes, then transfer them to a cooling rack to cool completely.