Leave the butter and egg at room temperature for 30 minutes.
In a medium-sized bowl, sift the flour and baking powder through a sifter (or fine strainer) twice. Over a work surface, rub the tea leaves into a fine powder by rubbing them between your fingers. Add the tea leaves and a pinch of salt into the flour mixture.
In a large bowl, cream the butter using a whisk. Add 6 tablespoons of the sugar into the butter in 2 stages and whisk until butter becomes white, about 5 minutes. In a small bowl, beat the egg and vanilla extract together. Slowly and gradually add the egg mixture into the butter mixture and whisk quickly until well incorporated. (If the egg mixture and butter mixture get separated while combining, add a pinch of flour to the mixture.)
With a wooden spoon, add the flour mixture and gradually mix until all of the ingredients are well blended. Shape the dough by hand into a 9-by-1 ½-inch-square block and wrap in plastic wrap. Chill in the refrigerator for 30 minutes.
Preheat the oven to 350 degrees.
Remove the dough from the refrigerator and cut into ¼-inch-thick square slices. If desired, place 2-4 tablespoons sugar in a small plate and coat the edges of each slice with the sugar.
Place the cookies 1 inch apart on an ungreased nonstick baking sheet. Bake in the oven for about 13–15 minutes until light golden brown. Remove from the oven, let cool, and serve.