In a small bowl, combine flour, tea, baking powder, and salt.
In a mixer, beat butter and sugar until fluffy.
Add the egg [and egg yolk] and combine.
Add the vanilla, [zest, and juice] to combine.
Add the flour mixture in batches until combined.
Divide dough in half and press into disks.
Wrap dough in plastic and refrigerate for at least 1 hour.
Heat oven to 350.
Roll dough 1/4 in thick [between plastic, wax paper, or parchment if you choose]
Cut cookies with cutters and place on parchment or silpat-lined baking sheets.
Bake 8-10 minutes.
While the cookies are baking, mix the sugar and tea for the topping.
Spread by the 1/4 teaspoonful onto warm cookies just out of the oven, spreading sugar about and pressing in slightly with the back of the spoon.
Cool cookies completely on a wire rack.