How to Make It
Stir together water, yeast, and 1 teaspoon of the sugar in a small bowl; let stand until foamy, about 5 minutes.
Combine milk, egg, salt, yeast mixture, 4 tablespoons of the butter, and remaining 2
tablespoons sugar in bowl of a heavy-duty stand mixer fitted with dough hook. Beat on medium-low speed until well combined, about 10 seconds. With mixer running on medium-low, gradually add flour, beating until all flour is incorporated. Continue beating until dough is smooth and elastic, about 4 minutes. Dough will be sticky. Transfer to a medium-size lightly greased (with cooking spray) bowl; cover with plastic wrap, and let rise in a warm place (80°F to 85°F) until doubled in volume, about 1 1/2 hours.
Turn dough out onto a lightly floured surface, and divide into 12 pieces (about 1 5/8 ounces each). Shape into balls, and place in a lightly greased 8-inch round pan. Cover with plastic wrap, and let rise in warm place until doubled in volume, about 45 minutes.
Preheat oven to 375°F. Gently brush rolls with 1 tablespoon of the butter. Bake in preheated oven until golden brown, 12 to 15 minutes. Brush rolls with remaining 1 tablespoon butter.