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To make the tangzhong: In a small saucepan, whisk together the ingredients until no lumps remain.
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Place the saucepan over medium heat and cook the mixture, stirring regularly, until thickened, paste-like, and the whisk leaves lines on the bottom of the pan. This should take about 2 to 4 minutes, depending on the strength of your burner.
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Remove from the heat and transfer to a large mixing bowl.
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To make the dough: Add the dough ingredients in the order listed to the mixing bowl. Mix until combined, then knead by hand, mixer, or bread machine until a soft dough forms.
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Place the dough in a lightly greased bowl, cover and let rise for 1 to 1 1/2 hours, until puffy but not necessarily doubled.
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To make the filling: In a medium bowl, combine the ingredients and mix until smooth.
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To assemble the loaf: On a lightly floured surface, gently deflate the dough, divide it into four pieces (about 150g each), and shape each piece into a ball. Cover and let rest for 10 minutes.
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Line a 9" springform pan with a piece of lightly greased parchment.
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Roll one piece of dough into a 6" x 12" rectangle, with the short edge facing you. Spread 2 heaping tablespoons of filling (about 50g) on the top half of the rectangle, leaving about 1/4" bare on the sides.
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Using a bench knife, cut the uncovered dough at the bottom into very thin strips (anywhere from 1/8" to 1/4" wide).
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Fold the long edges of the dough in to prevent filling from seeping out. Lightly brush the cut strips with water.
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Roll the covered dough down toward the uncovered strips to make a log about 6" long.
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Place the log, seam-side down, into the pan against its outside edge. Repeat with the remaining pieces of dough to form a complete circle.
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Cover the bread and let rise for 60 to 75 minutes, until puffy. Toward the end of the rising time, preheat the oven to 350°F.
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Uncover the loaf and lightly brush the bread with milk.
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Bake the wool roll for 28 to 32 minutes, until golden brown.
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Remove from the oven and cool in the pan on a rack until serving.
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Storage information: Store leftover wool roll bread, well wrapped, at room temperature for up to three days; freeze for longer storage.