Arrange rolls in a 9x13-inch baking dish.

Heat ice cream, butter, white sugar, and brown sugar in a saucepan over medium heat until ice cream is melted, sugars are dissolved, and sauce is warm, about 5 minutes; pour mixture over bread dough. Cover and let rise in a warm area until doubled, about 1 hour.

Preheat oven to 350 degrees F (175 degrees C).

Bake in preheated oven until rolls are golden brown, about 30 minutes.