In a medium saucepan, heat milk and 1⁄2 cup (120 grams) water over medium heat to scalding. (An instant-read thermometer should register 180°F/82°C.) Remove from heat, and add cubed butter; stir occasionally until butter is melted and an instant-read thermometer registers 120°F (49°C) to 130°F (54°C).
In the bowl of a stand mixer fitted with the paddle attachment, beat 2 cups (250 grams) flour, sugar, salt, and yeast at low speed until combined. Add warm milk mixture, and beat until combined. Add 1 egg (50 grams), beating until combined. With mixer on low speed, gradually add 2 cups (250 grams) flour, beating just until a shaggy dough comes together, stopping to scrape sides of bowl.
Switch to the dough hook attachment. Beat at low speed until a soft, somewhat sticky dough forms, about 24 minutes, stopping to scrape bottom and sides of bowl and dough hook; add up to remaining ¼ cup (31 grams) flour, 1 tablespoon (8 grams) at a time, if dough is too sticky. Turn out dough onto a clean surface; knead 5 to 6 times, 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, about 1 hour.