Preheat oven to 350 degrees F (177 degrees C).
Grease a loaf pan with butter or oil.
Add butter, sugar, salt, and baking powder to a large mixing bowl or to the bowl of a stand mixer. Cream together until light and fluffy. Make sure to scrap down the bowl every once in awhile so everything gets incorporated really well.
Next mix in the eggs and egg yolk one at a time. Make sure to scrape down the sides after you add each egg to ensure it mixes thoroughly.
Mix together your sour cream and vanilla extract in a bowl. Add half the sour cream to the mixing bowl. Mix until combined. Add half the flour. Mix until combined. Repeat this process until you get a soft batter.
Finish mixing the batter with a spatula (about 5-6 more mixes). This helps finish the mixing process and deflates some of the bubbles without overmixing it.
Spoon half the batter into another bowl. Sift matcha powder into 1/2 of the batter. Add the water. Mix until you see a nice uniform green color.
Now it’s time to form your pound cake! Spoon half the vanilla cake batter into the bottom of the loaf pan. Leave spaces in between the dollops for the matcha cake batter. Next spoon half the matcha cake batter into the spaces left. Use an offset spatula or knife to swirl the matcha and vanilla cake together. Repeat this process with the other half of both batters.
Once done swirling, tap the loaf pan on a flat surface to get rid of air bubbles and to make sure the batter is evenly distributed throughout the loaf pan.
Lastly, wet your knife and score the batter right down the middle to ensure a nice center crack while the pound cake is baking.
Bake for 60-70 minutes until a toothpick comes out clean. It should be nice golden brown all over.
Let it rest for 10 minutes before removing from the loaf pan.