Soften the butter until you can press it lightly with a finger and leave an indentation. Place it in a large bowl.
Add powdered sugar and mix with a whisk (or spatula) until fully combined. The mixture should become lighter in color and smooth.
Add the egg yolk and continue mixing until it's fully absorbed, creating a smoother texture.
Pour the 12g of cooled coffee liquid into the butter mixture and mix thoroughly. Ensure the coffee liquid is evenly incorporated.
In another bowl, combine cake flour and cocoa powder, then sift the mixture into the butter mixture.
Using a spatula, gently fold the flour mixture into the butter mixture. Avoid overmixing to prevent the dough from becoming tough.
Once the dough is mostly combined, knead it gently by hand until the dough becomes smooth.
Note: If the dough feels dry, add a few drops of milk or coffee liquid. If it's sticky, sprinkle a small amount of cake flour.