In a small bowl, combine together the warmed milk, sugar, and yeast. Leave it aside for a few minutes until bubbly.
In a stand mixer bowl, add in the flour, yeast mixture, salt, oil, egg, vanilla and matcha. Knead on low-medium speed until the dough comes together and is shiny, about 6-7 minutes. If it's too sticky, add in a little bit of flour. Try not to add in too much flour.
Transfer the dough into a lightly greased bowl and cover with a towel and leave to double in size in a warm location. Depending on the temperature of your room, it may take anywhere from 90 minutes to 2 hours.
Make the black sesame filing:
In a small bowl, combine together tahini, sugar, and black sesame powder. The mixture will be quite thick. If it's too thick, add in a little bit of the oil from the tahini to help loosen. Set aside.
Once the dough has risen, deflate the dough and transfer to a work surface dusted with a little flour. Use a rolling pin to roll it into a rectangle 15" by 10" in size.
With the long edge facing you, spread the black sesame filling evenly on the dough using an offset spatula. Carefully roll up the dough into a log. Divide and cut into 8 even pieces.
Place the pieces cut side up (with the swirl showing) onto a 8" or 9" round baking pan. Place a piece of plastic wrap over top and leave to double in size in a warm location.
Preheat oven to 350°F/177°C.
Once dough has risen, bake at 350°F/177°C for 25 minutes. Cover with foil for the last 5 minutes of the bake if the tops are browning too quickly.
Remove from the oven and let cool on a cooling rack.
Cool completely before adding the matcha glaze.
Make the matcha glaze:
In a bowl, combine the matcha, icing sugar, and a splash of milk. Stir the mixture until it's the consistency you like. Drizzle over top of the cooled buns.
Best eaten on the day it's made, however, it can be covered and stored at room temperature for up to 2 days, unless unglazed. Gently reheat in the microwave prior to serving.