Melt butter in a saucepan. Remove from heat and add tea leaves. Allow to steep for 20 minutes. Strain out tea leaves, squeezing out as much liquid from leaves. Place melted butter in refrigerator or freezer to harden.

Preheat oven to 400F. In the bowl of a mixer beat butter with sugar until combined. Add in egg, vanilla, and blend on medium until blended. Mix in flour, baking powder, and salt. Roll out dough between wax paper sheets 1/4 inch thick, cut with a 1-1/2 inch cookie cutter or cutter of your choosing. Bake on parchment lined baking sheets for 7-10 minutes, the bottoms of the cookies will be slightly firm and lightly golden. Allow cookies to cool completely on baking sheets. While cookies are baking, make the icing . When cookies are cooled, spoon icing onto each cookie.

To make icing: Mix powdered sugar with prepared thai tea and milk. You will want the mixture to be a little thick so the icing won't slide off of the cookie.