How to Make It
To prepare the dough, heat the milk in a small saucepan over medium heat until temperature reaches 110°-115°. Pour milk into a small mixing bowl; stir 1 tablespoon granulated sugar into warm milk. Sprinkle yeast over milk mixture and whisk to combine; let stand until foamy, about 5 minutes. Whisk in the egg yolks.
Combine the flours, salt, and remaining 5 tablespoons granulated sugar in the bowl of a stand mixer fitted with a dough hook attachment. Add the milk mixture. Turn the mixer on at medium-low speed; add the butter, one piece at a time, until all are fully incorporated. Increase speed to medium or medium-high, kneading until dough is soft and smooth.
Coat the bottom and sides of a large mixing bowl with butter. Form the dough into a ball and place in greased bowl, turning the dough to coat with butter from the bowl. Cover the bowl with plastic wrap and place in a warm place until doubled in volume, about 1 hour.
Punch the dough down after it’s risen; place on a lightly flour surface and let rest 15 to 20 minutes.
To prepare the filling, combine the butter, dark brown sugar, miso paste, and spices in the bowl of a stand mixer fitted with a paddle attachment; beat at medium speed until well combined.
To prepare the topping, combine the butter, dark brown sugar, corn syrup, and miso, in a medium saucepan over medium heat. Cook, stirring with a whisk, until mixture is melted and smooth; whisk in the cream. Pour the mixture into a greased 9-x13-inch baking pan; sprinkle the walnuts evenly over the caramel mixture.
To assemble the buns, roll the dough out into a 12-x18-inch rectangle. Spread the butter filling mixture evenly over the surface of the dough using a rubber spatula. Sprinkle the walnuts evenly over the butter mixture. Starting with the long side, roll the dough into a tight cylinder. Place seam side down and cut crosswise into 15 even slices.
Place the rounds on prepared topping in baking pan, crowding them so they touch. Loosely cover pan with plastic wrap and let stand in a warm place for 1 hour. Transfer buns to refrigerator for at least 2 hours or overnight.
Preheat oven to 350°. Remove plastic wrap from the buns. Bake on center wrack, rotating pan halfway through baking, until buns are golden brown and topping is bubbling in the pan, 45 to 50 minutes. Allow to cool in pan 3 minutes before carefully inverting onto a serving tray or rimmed baking sheet. Serve warm.