Bloom the yeast. In a stand mixer bowl, whisk the warm milk (180 g / ¾ cup), sugar (50 g / ¼ cup), and instant yeast (7 g / 2¼ tsp). Let sit 5 minutes until foamy.

Mix the dough. Add the eggs and salt (6 g / 1 tsp). Add the bread flour (420 g / 3⅓ cups) and mix on low with the dough hook until a shaggy dough forms.

Knead in the butter. Knead on medium 5 minutes, then add the softened butter (85 g / 6 Tbsp) a piece at a time, kneading until fully absorbed and the dough is smooth and elastic, about 8–10 more minutes.

First rise. Shape into a ball, place in a greased bowl, cover, and let rise in a warm spot 1–1½ hours, until doubled.

Make the filling. Beat the softened butter (57 g / 4 Tbsp), sugar (67 g / ⅓ cup), and matcha powder (15 g / 2 Tbsp) into a smooth paste.

Roll and fill. Roll the dough into a 16x10-inch rectangle. Spread the matcha filling to the edges and scatter the chopped white chocolate (85 g / ½ cup) evenly over the top.

Roll and twist. Starting from a long edge, roll the dough into a tight log. Slice the log in half lengthwise, exposing the swirled layers, then twist the two halves around each other, keeping the cut sides facing up as much as possible.

Shape and refrigerate. Tuck the twisted dough into a buttered 9x5-inch loaf pan, cover tightly, and refrigerate overnight, 8–12 hours.

The next day, let it rise. Remove the pan from the fridge and let sit at room temperature 1–1½ hours, until puffy.

Bake. Preheat the oven to 350°F. Bake 35–40 minutes, tenting loosely with foil after 20 minutes if the top is browning too fast.

Make the syrup. While the babka bakes, simmer the sugar (100 g / ½ cup), water (120 g / ½ cup), and yuzu juice (30 g / 2 Tbsp) in a small saucepan 3–4 minutes, until slightly syrupy.

Glaze and finish. Brush the warm babka generously with the yuzu syrup as soon as it comes out of the oven. Let cool completely, then whisk the powdered sugar (90 g / ¾ cup) with a tablespoon or two of yuzu juice and drizzle over the top.