Step 1
Dissolve yeast and 1 teaspoon sugar in 1/2 cup warm water in a bowl; let stand until mixture is foaming about 10 minutes.
Step 2
Stir warm milk 6 tablespoons sugar salt and remaining 1/2 cup warm water into yeast mixture. Gradually whisk 2 cups flour into yeast mixture until smooth. Add remaining 3 1/2 cup flour egg 2 tablespoons and 2 teaspoons vegetable oil to flour-yeast mixture; stir until dough is soft.
Step 3
Turn dough onto a floured work surface; knead until smooth and elastic 6 to 8 minutes. Place dough in a greased bowl turning once so top of dough is greased. Cover bowl with a damp towel and let rise in a warm room until doubled in size about 1 hour.
Step 4
Punch dough and divide in half. Roll each half on a floured surface until 1/3 to 1/2-inch thick. Cut dough using a floured 2 1/2-inch round cutter. Brush each dough circle with melted butter.
Step 5
Make an off-center crease in each dough circle using the dull edge of a table knife. Fold along crease so larger half is on top; press along folded edge.
Step 6
Grease a baking sheet.
Step 7
Arrange folded dough circles 2 to 3 inches apart on the prepared baking sheet. Cover with a damp towel or plastic wrap and let rise until doubled in size about 30 minutes.
Step 8
Preheat oven to 375 degrees F (190 degrees C). Remove towel or plastic wrap from dough.
Step 9
Bake in the preheated oven until rolls are golden brown 15 to 20 minutes. Transfer rolls to a wire rack to cool.