Preheat oven to 400°. Butter a 10-inch skillet or cake pan.
In a large bowl whisk together flour, matcha, baking powder, baking soda, and salt. In a small bowl whisk together starter, milk, and oil until starter has dissolved. Add wet ingredients into dry ingredients and mix until a shaggy dough forms. Turn out onto a lightly floured surface and knead until a smooth dough forms, about 2-3 minutes.
Add more flour to surface as needed and roll out dough to a roughly 10x15-inch rectangle. Spread red bean paste over the top of the dough, leaving a small border of about 1/4-inch. Roll dough tightly into a cylinder, starting from one of the long edges. Cut cylinder into 8 rolls with a serrated knife. Place into buttered pan.
Bake for 22-25 minutes, until lightly browned on edges. While baking, place cream cheese in a small microwave safe bowl. Microwave for 15-30 seconds until very soft. Stir until smooth. Beat in the powdered sugar then stir in 1 tsp milk and mix until smooth.
Allow buns to cool for about 5 minutes before frosting. Serve warm or at room temperature.