In a medium saucepan, heat milk and 1⁄2 cup(120 grams) water over medium heat to scalding.(An instant-read thermometer should register180°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) to130°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 egg, 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 1⁄4 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.Proceed with recipes that follow.