Preheat the oven to 375 degrees. Beat the butter and sugar until fluffy. Stir in tea leaves until well combined. Beat in the egg, then carefully fold in the flour.
Roll the dough into a long cylinder. Flatten the cylinder into a rectangular shape, pressing granulated sugar and more mint leaves into the sides. Put the dough in plastic wrap and chill for about an hour, until the dough is firm enough to slice.
Using a sharp knife, cut the dough cylinder widthwise into 1/4" slices and place, slightly apart, on the baking sheets. Bake for 15-18 minutes until slightly browned. Transfer to a wire rack to cool completely.