Wash hands for 20 seconds, according to CDC guidelines. Preheat oven to 425 F.
Place two bags of the tea in the hot water. Let the tea steep. After 4 to 5 minutes, remove and discard the tea bags. Set the brewed tea aside to cool completely.
Combine the flours, granulated sugar, baking powder, baking soda, and salt in a medium bowl. Whisk thoroughly.
Using a pastry cutter, blend the grated butter into the dry ingredients. Do not use the cutter too vigorously. Bits of butter should still be visible. The mixture should look it has tiny pebbles or large grains of sand.
Cut open the remaining four tea bags. Add the ground tea leaves to the butter-flour mixture and stir gently to combine.
In a 2-cup liquid measure, combine the buttermilk, egg,*(see notes) and vanilla. Beat lightly, then pour the liquid ingredients into the butter-flour-tea mixture. Combine with a spatula until a soft, ragged dough forms.
Turn the dough out onto a floured sheet of parchment or wax paper. Knead gently a few times until the dough can be shaped into a rectangle about 1½ inches thick.
Using a large, floured knife, cut the dough rectangle into thirds. Cut each third into 4 squares, so you end up with 12 squarish scones. With a small spatula, place each scone on the prepared baking sheet.
Bake for 12 to 15 minutes.
Remove from oven when the tops are golden and the scones are baked through.
Make the glaze while the scones are cooling.