Make the Dough

1. Warm the milk until it feels like bath water. Stir in yeast and sugar, and let stand for a few minutes until foamy.
2. Add eggs, melted butter, salt, and flour. Mix until a shaggy dough forms.
3. Knead the dough until smooth and stretchy. If sticking, add a little more flour.
4. Cover the dough and let it rise until doubled in size, about 60 to 90 minutes.

Prepare the Filling

1. Mix brown sugar and cinnamon in a bowl.
2. Roll out the dough and spread softened butter over it. Sprinkle the sugar mixture evenly and top with diced apples.
3. Press apples gently into the dough.
4. If apples are juicy, toss them with a teaspoon of flour.

Roll, Slice, and Proof the Rolls

1. Roll the dough tightly from the long side into a log.
2. Slice the rolls using unflavored dental floss or a sharp knife.
3. Place the rolls in a buttered baking dish with space between them.
4. Cover and let proof until puffy and touching.

Bake the Rolls

1. Preheat oven to 350°F (175°C) and bake rolls until golden and centers are set, about 25 minutes.
2. If the tops brown too quickly, cover with foil for the last few minutes.
3. Let rolls cool for about 10 minutes before frosting.

Make the Frosting

1. Beat softened cream cheese and butter until smooth.
2. Add powdered sugar, vanilla, and milk; mix until fluffy.
3. Spread on warm rolls.