Refrigerate cookie stamps.
Empty the chai from teabags and grind finer using a spice grinder or mini chopper so no twiggy stems or large pieces of black tea remain; set aside.
In a medium mixing bowl, combine the flour, chai seasoning, and salt.
In the bowl of an electric mixer fitted with the paddle attachment, add the butter, dark brown sugar, and the finely ground chai tea. Beat on medium speed until fluffy. Add large egg and vanilla; beat until combined.
Add the flour mixture to the creamed mixture. Mix on low speed until the ingredients are just incorporated. Increase to medium speed until a thick dough forms and the beaters clean the sides of the bowl.
Cover the bowl and refrigerate for 30 minutes.
Set the bowl of dough out at room temperature for 5 minutes to soften before you begin.
Preheat the oven to 350°F. Line two cookie sheets with parchment paper. Cover work surface with silicone baking /rolling mat or large sheet of parchment paper.
Use a 1/4 cup measuring cup (or #16 / 4 tablespoon cookie scoop) to portion out dough and roll into a balls.
Add granulated sugar to a shallow bowl or plate; roll dough ball in the sugar. Place on the parchment-lined work surface.
Press a chilled cookie stamp down onto the dough in a circular motion until excess dough squeezes out and is visible on all sides of the cookie stamp. Gently pry the edges of the dough from the stamp with your thumb on all sides until the cookie releases. The colder your cookie stamps are, the easier the dough will release so return stamps to fridge or freezer for a quick chill if needed.
Trim excess dough away from the shape using a knife, if needed. Transfer stamped cookie to prepared cookie sheet with spatula.
Repeat with remaining dough. You should get 14 cookies using every bit of the dough, so return scraps and add back to dough mixture to re-roll as you go.
Chill the cookies in the refrigerator for 15 minutes, then bake for 12-15 minutes or until lightly puffed and fragrant. Let cool on the pans until firm enough to transfer to a wire rack to cool completely.
Store in an airtight container up to 5 days