Preheat the oven to 320°F (160°C) and line an 18 cm loaf pan with parchment paper.
Whisk together the cake flour and baking powder in a medium-sized bowl; set aside.
Melt the salted butter in a water bath: place a glass pan with the butter directly in a saucepan filled with 1 to 2 inches of water, and heat until the butter is fully melted. Remove from heat and cover to keep warm.
In a separate bowl, whip the eggs and granulated sugar on high speed with a hand mixer until pale and thick, until the batter holds a figure 8 shape about 1 cm high. Switch to low speed and mix for 30 seconds more. Set aside.
Sift about ⅔ of the flour mixture into the egg batter. Fold with a cutting, scooping motion, turning the bowl with your other hand, until no flour is visible.
Add the sour cream to the melted butter. Stir together until smooth.
Sift the remaining flour mixture into the butter mixture and fold with a spatula until no dry flour remains. Mix briefly with your hand mixer.
Add two scoops of the egg batter into the butter mixture and mix on low speed for about 30 seconds.
Pour the butter mixture into the remaining egg batter and fold again with a cutting, scooping motion.
Add the yuzu cha, brought to room temperature, and fold until just combined. Be careful not to overmix.
Pour the batter into the prepared pan and drop it on the counter 3 to 4 times to release air bubbles.
Lay two thin slices of butter, for the center line, on top of the batter. Make sure they are connected to form one solid line.
Bake at 320°F (160°C) for 35 minutes, until a toothpick inserted in the center comes out clean or with a few moist crumbs.
Cool in the pan. Once the cake is cool enough to handle, gently remove it from the pan and parchment paper.