Gather all the ingredients. It's important that the butter, eggs, and milk are all at room temperature. Center a rack in the oven and preheat it to 350ºF (180ºC). For a convection oven, reduce the cooking temperature by 25ºF (15ºC).
Use the residual butter on the butter wrapper to grease the pan (8½ x 4½ x 2¾ inches). Then, place the parchment paper inside the pan (the paper will stick to the butter).
To Make the Batter
Put the room-temperature butter in a large bowl. Use an electric hand mixer (or stand mixer) to beat it on medium speed until it is light and fluffy, about 1-2 minutes. The butter will be pale in color and have lots of little tails forming around the beaters. Tip: This process adds air to the mixture and is crucial for a light and delicate cake texture.
Add the sugar to the whipped butter. Cream the butter and sugar thoroughly on medium (not high) speed, about 5 minutes, until it is light and fluffy. The color is pale and the sugar is completely dissolved. Tip: The sharp sugar grains cut through the butter and create the tiny air pockets that aerate the batter and cause leavening. This process is very important for the light and delicate texture of the pound cake.
Crack the eggs in a small bowl and whisk well.
Add the whisked eggs, 1 Tbsp at a time, to the butter mixture and beat well after each addition. Repeat until all the egg is incorporated. IMPORTANT: You must add and blend only a very small amount of egg at a time to achieve a smooth mixture (not a curdled mixture). Tip: The eggs contain water, while the yolks and the butter contain fats. Remember, oil and water will not mix without an emulsifier (in this case, the yolks) that suspends fat molecules in water to make a smooth mixture.
If there is a slightly curdled appearance to the batter after adding the eggs, don’t worry. The emulsification is usually complete enough that the batter will become smooth when you add the flour. The flour helps to absorb some of the excess water, too.
Next, add the dry ingredients in three stages. Put the cake flour, baking powder, and salt in a fine-mesh sieve. Sift one-third of these dry ingredients into the bowl of the egg mixture. Switch to a silicone spatula (or use a mixer on the lowest speed) and combine the mixture by hand so you can scrape the bottom of the bowl to get any dry pockets of flour.
Now, add another one-third of the dry ingredients and mix again.
Finally, stir in the remaining dry ingredients. Mix it just until the batter is smooth. Tip: Even though we are using a low-protein cake flour, excess mixing will develop the gluten and the cake will rise nicely in the oven, then sink as soon as you pull it out. A sunken cake has a tougher crumb with dense, moist, and gluey streaks.
To Incorporate the Matcha
Next, make a paste with the matcha: Heat the milk in a microwave or saucepan until warm (roughly body temperature). Gradually add the milk, 1 Tbsp at a time, to the matcha in a medium bowl. Whisk well until combined. Tip: Warm liquid is easier to blend with matcha.
Add one-third of the batter to the bowl with the matcha.
Use a silicone spatula to fold the batter into the matcha paste just until the it's smooth and homogenous. Do not overmix.
Now, combine the green and yellow batters to create a marbled pattern. Add the matcha batter to the original yellow batter in 6-8 separate dollops scattered around the bowl. To swirl the two batters, use a silicone spatula to scoop the batter from the bottom of the bowl and fold it onto itself while rotating the bowl a quarter turn. Repeat this two more times only.
Pour the batter into the pan without mixing the batter, keeping the swirl effect. Tap the cake pan on the countertop once to release an air pockets.
Using an offset spatula, smooth out the surface of the batter without mixing too much.
Put the cake pan in the oven. Lower the oven temperature to 340ºF (170ºC) and bake for 50 to 60 minutes.
After 15 minutes, open the oven and quickly score the top of the cake with a sharp knife. (Please read the blog post why we do this). Continue to bake.
The cake is done when a wooden skewer inserted in the center of the cake comes out clean.
Remove from the oven and allow the cake to rest in the pan for 15 minutes on a wire rack. Then, take the cake out of the pan to cool completely. Enjoy!
You can keep the leftovers in an airtight container (or wrap in plastic) and store it in the refrigerator for up to 3 days and in the freezer for up to 3 months.