In a medium bowl, combine warm milk, granulated sugar, and active dry yeast. Allow to sit for about 5-10 minutes until foamy.

Add melted butter and beaten egg to the mixture, whisking together.

In a separate bowl, whisk together flour and salt. Gradually stir into wet mixture until a shaggy dough forms.

Knead the dough on a floured surface for 6-8 minutes until smooth and elastic.

Place the dough in a greased bowl, cover, and let rise for 1 to 1.5 hours until it doubles in size.

Melt butter in a skillet and sauté diced apples for 2-3 minutes. Stir in brown sugar, cinnamon, and nutmeg. Allow to thicken.

Punch down the risen dough and roll out into a large rectangle. Spread remaining melted butter and cooled apple filling over the dough.

Starting from one edge, tightly roll the dough into a log and seal the seam.

Slice the rolled dough into 12 equal pieces and place in a greased baking dish.

Cover the dish and let rolls rise for 30-45 minutes until puffy.

Preheat the oven to 350°F (175°C).

Bake rolls for 25-30 minutes until golden brown. Cover with foil if they brown too quickly.

Cool in the pan for 10-15 minutes, then frost the rolls with cream cheese frosting.