Pour milk into a glass 2-cup measuring cup and heat in the microwave until it starts to boil and climb the sides, about 1 minute. Add butter, 1/4 cup sugar, and salt to the scalded milk; set aside to cool until it gets below 110 degrees F (45 degrees C).
Dissolve yeast and 1 teaspoon sugar in warm water in a large bowl. Let stand until the yeast softens and begins to form a creamy foam, about 10 minutes.
Pour milk mixture into the yeast mixture; add 2 cups bread flour and egg. Stir the mixture with a wooden spoon until smooth. Add remaining flour, 1/2 cup at a time, mixing thoroughly after each addition, until the dough is smooth and a little tacky.
Turn dough out onto a sheet of flour-dusted waxed paper and lightly knead to pull dough together; shape into a ball. Place dough in a large, lightly-oiled bowl, and turn to coat. Cover with a towel and let rise in a warm place for about 30 minutes.
Line a baking sheet with parchment paper. Divide dough into thirds. Break each third into six evenly sized balls and arrange onto prepared baking sheet. Cover balls with a towel to rise further for another 30 minutes.
Preheat oven to 350 degrees F (175 degrees C).
Bake in preheated oven until browned, about 15 minutes.