Mix warm milk, sugar, and yeast in a large bowl and let it sit until foamy. Add egg, butter, oil, and salt before gradually mixing in flour to form a soft dough.
Knead the dough for about 8–10 minutes until smooth and elastic. The dough should feel soft and slightly tacky rather than dry.
Place the dough into a greased bowl, cover it, and let it rise until doubled in size, about 1 hour depending on room temperature.
Divide the dough into 12 equal pieces and shape into smooth balls. Arrange them in a greased baking dish and let them rise again until puffy.
Bake at 375°F for 18–20 minutes until golden brown. Brush the hot dinner rolls with melted butter immediately after baking for extra softness.
Cool slightly before serving so the inside texture finishes setting while staying soft and fluffy.