In a large bowl, beat butter and powdered sugar until smooth.
Mix in flour, followed by tea and vanilla, to form the cookie dough.
Cool in refrigerator for 20 minutes to prevent dough from sticking.
Roll dough to 1/2-inch thick on a lightly floured surface, then cut into shapes using either a knife for long, rectangular cookies or cookie cutters for other shapes.
Place cookies 1/2 inch apart on a cookie sheet, then bake for 12 to 15 minutes or until cookies are set.