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Gather all the ingredients. It‘s important that the butter, eggs, and milk are all at room temperature.
Preheat the oven to 350ºF (180ºC).
Grease the pan and line it with parchment paper.
Beat the butter in a large bowl until light and fluffy.
Add sugar to the whipped butter and cream thoroughly.
Crack the eggs in a small bowl and whisk well.
Add the beaten eggs to the butter mixture, 1 Tbsp at a time, beating well after each addition.
Add the dry ingredients in three stages, folding the mixture by hand until smooth.
Make a paste with the matcha and warm milk, whisking until combined.
Add one-third of the batter to the matcha paste and fold until smooth.
Combine the green and yellow batters to create a marbled pattern.
Pour the batter into the cake pan without mixing.
Lower the oven temperature to 340ºF (170ºC) and bake for 50–60 minutes.
Check for doneness with a wooden skewer.
Allow the cake to rest in the pan for 15 minutes, then cool completely.