Yield: three layer 6-inch cake
Bring milk to a simmer. Add tea and steep for 30 minutes. Strain out tea. Squeeze out as much liquids from tea as possible. Measure remaining liquid. Add additional milk as necessary until you have 3/4 cup liquids.
Preheat oven to 350 degrees F. Lightly butter and flour three 6-inch round cake pans. Line with parchment paper. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, combine 2 cups flour (reserve remaining 1/2 cup), sugar, baking powder, and salt. Run mixer on speed. Add butter in three additions. Continue to mix on low speed until mixture is crumbly.
In another bowl, combine infused tea milk, eggs, and egg white. Add half of liquid to mixing bowl. Mix on medium speed until incorporated. Scrape down bowl as needed to ensure thorough mixing. Add remaining half of liquid and mix until batter is combined. The batter will look curdled. Add reserved 1/2 cup flour and mix until batter comes together.
Evenly distribute batter among prepared cake pans. Bake for 30-35 minutes until toothpick inserted in center of cake comes out clean. Allow cake to cool in pan for 10-15 minutes. Run an offset spatula along the sides of cake pan to loosen cake. Invert cake onto a wire rack and allow to cool to room temperature.
Combine water and sugar in a small sauce pot. Bring to a boil until sugar has dissolve. Remove from heat. Add tea and steep for 20 minutes. Strain out tea. Cool to room temperature and keep store in the fridge until ready to use.
Warm milk to a simmer. Remove from heat. Add tea bags and let steep for 15 minutes. Squeeze out as much liquid from tea bags. Discard tea bags. Keep chilled until ready to use.
In the bowl of a stand mixer fitted with a paddle attachment (or using an electric hand mixer), cream butter until smooth. Add powdered sugar and mix until incorporated. Scrape down bowl as needed. Add vanilla, salt, and milk tea concentrate. Mix until thoroughly combined.
Combine black tea simple syrup and milk tea concentrate before assembling cake.
Fill a heavy bottomed sauce pot with 5 cups water. Bring to a boil. Add dried tapioca pearls. Stir to combine and distribute pearls. Allow mixture to continue boiling for about 40 minutes. At this point the pearls should look gelatinous. Reduce heat to a simmer and cook for another 15 minutes until peals are soft and chewy. Add brown sugar and continue to simmer until sugar has dissolved. Remove from heat and allow tapioca pearls to cool. As mixture cools, the syrup will thicken. Keep warm until ready to use.
Place one cake round on cake board (or serving plate). Brush cake layer with soaking syrup. Spring a thin layer of buttercream over cake layer. Repeat with second and third cake layer.
Spread buttercream around the exterior of cake to seal in any crumbs. Chill in the fridge for 15 minutes to set up. Add another thin coat of buttercream all over cake.
Keep cake chilled. Allow cake to sit at room temperature for 15 minutes before serving. Just before slicing, add warm tapioca pearls to top of cake. Serve cake slices with additional tapioca pearls, if desired.
Cake can be made two days in advance.
If you have leftovers of the assembled cake, remove and discard boba before storing cake in the fridge.
All images and text © The Little Epicurean