Preheat oven to 350°. Grease the bundt pan using a pastry brush to ensure all the nooks and crannies of the mold are buttered. Pour a teaspoon of sugar and bang the pan around to ensure the sugar covers all of the pan in a thin layer.
In a large mixing bowl, cream together the butter with the sugar until it is pale and fluffy (about 3 minutes.
Add the eggs, vanilla extract and milk to the creamed butter bowl. Mix until incorporated.
In a separate medium bowl, whisk together flour, baking powder and salt. Scoop half of this mixture into the batter bowl and mix until combined.
To the leftover flour mixture bowl, sift in the matcha powder. Scoop half of the batter mixture into the matcha bowl and mix.
Grab the 6-cup greased bundt pan, and using a 1/4 cup measure for each batter, spoon 1/4 cup of the vanilla batter into the pan and then scoop 1/4 cup of the matcha batter on top of that. Continue alternation batters along the bundt pan until no more batter is left. Take a knife or toothpick and swirl the batter around a few times to get some marbling on top.
Bake in oven for 45-50 minutes (until a knife or toothpick inserted comes out clean).
Let cool and slice and enjoy!