Prepare a 6-cup Bundt pan. I used the Jubilee loaf pan.
In a bowl, sift together the flour, baking powder and salt. Split the mixture equally among two bowls (I weigh each to be exact). Add the matcha to one bowl and use a hand whisk to combine.
Use a stand mixer fitted with the paddle attachment to cream the butter, sugar and vanilla bean paste. Add the eggs, milk and vanilla and mix until thoroughly combined.
Add half the butter mixture to the matcha mixture (again, I weigh each to be exact). Mix until well combined.
Combine the melted chocolate to the other half of the butter mixture and add to the remaining flour mixture. Mix until well combined.
Scoop alternating colours and place randomly into the Bundt pan. Bake for about 50 to 60 minutes. Check for doneness with a toothpick or cake tester.
Remove from the oven when finished and allow to cool for 10-15 minutes in the pan, on a cooling rack. Then place the cooling rack over the pan and invert to release the cake. Allow to cool completely. Chocolate drizzle optional, but... DUH!!