Combine warm milk, yeast, and a spoonful of sugar and let stand for 5 minutes.
Mix in the remaining sugar, egg, melted butter, salt, and flour to form a soft dough.
Knead until smooth, cover, and let rise until doubled.
Roll the dough into a rectangle and spread with softened butter.
Sprinkle with brown sugar, cinnamon, and diced apples.
Roll tightly, slice into 9–12 pieces, and arrange in a greased baking dish.
Let rise for another 30 minutes, then bake at 350°F (175°C) for 25–30 minutes.
Drizzle the warm rolls generously with caramel sauce.