Preheat oven to 350°F. Spray bundt pan with cooking spray.
Use a whisk to combine flour, baking powder, baking soda, and salt. Sift together. Set aside. In a small bowl combine the espresso powder, cocoa and 1/3 cup of the sugar with 1/4 cup of water. Whisk until smooth. Set aside. In another small bowl, whisk whole egg with egg white. Set aside.
Cut the butter into pieces and place in an electric mixing bowl. Beat for 1 minute to soften. Gradually add remaining 1 cup of sugar and beat at high speed for about 3 minutes. Add in egg mixture, beating constantly for about 2 minutes. On low speed, beat in a third of the flour mixture. On medium-high speed, beat in half of the yogurt. On low speed, beat in half of the remaining flour. On high speed, beat in the rest of the yogurt and the vanilla. On low speed, beat in the remaining flour.
Measure out 1 1/2 cups of yogurt batter and mix into the cocoa mixture. Set aside. Add matcha powder to the rest of the yogurt batter in the mixing bowl.
Use a large spoon to fill the bottom of the pan with about three quarters of the green batter placed in dollops. Cover the green batter with dollops of chocolate batter. Top the chocolate batter with small dollops of green batter spaced so that the chocolate batter shows through. Use a table knife to marble the batters together with a circular or zigzag motion; be careful not to blend them too much.
Bake for 45-50 minutes for cake, or until the cake starts to pull away from the sides of the pan and a toothpick inserted in comes out clean.
Cool for 10-15 minutes on a rack. Unmold the cake. Cool completely before serving or storing.
The nutrition information provided are only estimates based on an online nutritional calculator. This is not a comprehensive list of all the nutrients in the recipe (i.e., does not include vitamins, cholesterol, etc). I am not a certified nutritionist. Please consult a nutritionist or doctor for accurate information and any dietary restrictions and concerns you may have.