Making the dough

1. Warm the milk until it feels like a warm bath, not steaming. Stir in a pinch of sugar and the yeast. Let it sit for 5 to 10 minutes until foamy.
2. Mix in sugar, melted butter, egg, flour, and salt. Knead until the dough looks smooth and elastic.
3. If the dough feels sticky, add a spoon of flour at a time. If it feels dry, add a tiny splash of milk.

Letting the dough rise

1. Put the dough in a greased bowl, cover, and let it rise until doubled, about 1 hour in a warm kitchen.

Preparing the apple filling

1. Dice apples into small pieces and toss them with cinnamon and a spoon of sugar.
2. Optionally sauté them for 3 to 5 minutes with a little butter for extra softness.

Rolling, filling, and slicing

1. Roll the dough into a rectangle on a lightly floured counter.
2. Spread softened butter all over, sprinkle brown sugar and cinnamon evenly, and scatter the diced apples on top.
3. Roll it up tightly from the long side and slice into equal pieces.

Second rise and baking

1. Place rolls in a buttered baking dish, cover, and let rise again until puffy, about 30 to 45 minutes.
2. Bake until lightly golden and the center looks set, about 30 minutes. Cover with foil if they brown too quickly.

Making the frosting

1. Mix softened cream cheese, softened butter, powdered sugar, vanilla, and a pinch of salt.
2. If it is too thick, add a teaspoon of milk; if too thin, add more powdered sugar.
3. Frost the rolls while they are warm.