Grease two 6-inch pans and line with parchment. Preheat oven to 350° F.
Scald the milk, add the tea, and let steep, covered, for 5 minutes. Remove the tea bags.
In the bowl of a stand mixer fitted with the paddle attachment, combine the flour, sugar, baking powder, and salt. Add the soft butter and mix on low until the butter breaks down into pea-sized crumbs.
In a separate bowl, combine strained milk, egg whites, and vanilla. Add all but 1/4 cup of liquid ingredients to the stand mixer and blend on medium until light and fluffy, about 3 minutes. Pour in remaining milk mixture and blend until combined, 1 minute.
Divide batter evenly between the two pans and bake for 25-30 minutes, until golden brown and beginning to pull away from the sides of the pan. Allow to cool completely.
Invert and remove from pans, removing parchment from the bottom of the cake.