Microwave milk for 90 seconds to 2 minutes until very hot. Steep tea bags for 20 minutes. Squeeze out as much liquid from tea bags. Remove tea bags. Stir in egg whites and vanilla paste. Set aside.
Preheat oven to 350° F. Lightly grease and flour two 6-inch cake pans. Line with parchment paper and set aside.
Sift together cake flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, cream together softened butter and sugar. Add ⅓ of dry flour mixture. Mix on low speed. Add ½ of liquid mixture. Continue to mix on low speed and add another ⅓ of dry flour mixture. Add remaining liquid mixture. Mix on low and add remaining ⅓ of dry flour mixture. Scrape down bowl as needed to ensure thorough mixing. Batter should be smooth.
Divide batter between two prepared cake pans. Level batter using the back of a spoon or a mini offset spatula. Bake for 30-35 minutes, rotating once halfway through baking. Allow to cool in pan for 5 minutes before unmolding. Place cake on wire rack and allow to cool to room temperature