In a small saucepan, heat milk over medium heat until scalding. (An instant-read thermometer should register 180°F/82°C.) Let cool until an instant-read thermometer registers 110°F (43°C) to 115°F (46°C).

In a small bowl, whisk together warm milk, 1 teaspoon (4 grams) sugar, and yeast. Let stand until foamy, 5 to 10 minutes.

In the bowl of a stand mixer, whisk together 11⁄2 cups (190 grams) flour, salt, and remaining 3 tablespoons plus 2 teaspoons (44 grams) sugar by hand. Add warm yeast mixture, Tangzhong, and egg; using the paddle attachment, beat at low speed until well combined. With mixer on low speed, gradually add 1 cup (127 grams) flour, beating just until a shaggy dough comes together and stopping to scrape sides of bowl.

Switch to the dough hook attachment. Beat at low speed until dough is tacky, elastic, and slightly smooth, about 8 minutes; add up to remaining 1⁄4 cup (32 grams) flour, 1 tablespoon (8 grams) at a time, if dough is too sticky. Add butter, 1 tablespoon (14 grams) at a time, beating until combined after each addition (about 5 minutes total). Scrape sides of bowl and dough hook. Beat until dough is completely smooth and passes the windowpane test, about 12 minutes. (See Note.) Turn out dough onto a clean surface, and shape into a smooth round.

Lightly oil a large bowl. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 45 minutes to 1 hour.