Combine boiling water and tea leaves in a bowl; allow to steep for about 5 minutes. Set aside to cool.

Preheat oven to 350 degrees F (175 degrees C). Spray a cake pan with cooking spray.

Mix vegetable oil in to tea. Strain tea leaves from tea using a strainer or paper coffee filter.

Whisk eggs in a bowl; add sugar and mix well. Sift flour and baking powder together in a separate bowl.

Mix half of the flour mixture into the egg mixture, stirring quickly. Add half of the cooled tea mixture to flour-egg mixture, mixing well. Add the remaining flour mixture to the batter, mixing well. Stir the remaining cooled tea mixture to batter, mixing well. Pour batter into the prepared pan and place on top of a baking sheet.

Bake in the preheated oven until a toothpick inserted in the center of the cake comes out clean, about 35 minutes. Cool cake for 20 minutes.

Spread frosting onto cake and sprinkle green tea powder on top.