Japanese Milk Bread

First, make the tangzhong (cooked flour paste): place water and 1/4 cup each of the flour and milk in a small saucepan. Whisk until smooth. Heat over medium-low, whisking constantly, until mixture has thickened to a pudding-like consistency, about 3 minutes (mixture will go from liquidy to thick in a few seconds, so don't walk away). Transfer mixture to a small bowl, and press plastic wrap directly onto surface. Let tangzhong cool to warm room temperature, about 20minutes.

Place egg, sugar, salt, yeast, cooled tangzhong, and 1/2 cup of the milk in bowl of a stand mixer fitted with a dough hook. Beat on low speed until combined, about 30 seconds. Gradually add remaining 2 2/3 cups flour, beating until all flour is incorporated, about 5 minutes. Add butter pieces; increase mixer speed to medium-low, and beat until dough is smooth and elastic, about 6 minutes. (Dough will be sticky.)

Transfer dough to a large bowl lightly coated with cooking spray. Cover tightly with plastic wrap, and let stand at room temperature until doubled in size, about 1 hour.

Preheat oven to 350°F. Lightly coat an 8 1/2- x 4 1/2-inch loaf pan with cooking spray. Turn dough out onto a lightly floured work surface. Dust top of dough lightly with flour, and roll into a 13-by-10-inch rectangle. Starting from 1 short side, roll dough into a cylinder. Place dough log in prepared loaf pan, tucking ends under to fit pan. Gently press dough to shape into pan, gently pushing dough into corners and leveling top. Cover loosely with a piece plastic wrap lightly coated with cooking spray. Let stand at room temperature until loaf has risen just above the lip of the pan, 25 to 35 minutes.

Uncover loaf, and gently brush with remaining 1 1/2 teaspoons milk. Bake until bread is golden brown and a thermometer inserted into thickest portion of loaf registers 205°F, 35 to 45 minutes, tenting with aluminum foil during last 10 minutes if needed to prevent over browning. Remove from oven. Brush top of hot loaf with melted butter. Let bread cool in pan 10 minutes. Remove from pan, and let cool completely on a wire rack, about 2 hours. Slice and serve.