Dough: In the bowl of a stand mixer, combine warm apple cider, yeast, and sugar. Let sit for 5-7 minutes to allow mixture to bubble and activate. Whisk in milk, egg, egg yolk, and brown sugar. Attach dough hook to stand mixer.
In a large bowl, whisk together flour, salt, nutmeg, and cinnamon. Add 1/3 of flour mixture to mixing bowl. Mix on low speed until flour is incorporated. Add another 1/3 of flour mixture. Continue to knead on low speed adding softened butter one tablespoons at a time. Add remaining flour mixture and knead until dough is smooth and cleans the sides of the bowls.
Transfer dough to a lightly greased large bowl. Cover with plastic wrap and let dough rest at room temperature for about an hour, until dough has doubled in volume.
Apple Filling: Meanwhile, combine chopped apples with apple cider, salt, and ground cinnamon. Set aside while you roll out dough. In a small bowl, combine brown sugar, sugar, and cinnamon.
Punch down risen dough. Transfer to a lightly floured work surface. Roll dough into a 20 x 14-inch rectangle. Spread softened butter over dough. Sprinkle brown sugar cinnamon mixture over dough.
Strain chopped apples from liquid mixture. Set aside and save liquid mixture. Distribute chopped apples over dough. Roll dough into a tight log, starting at the longer side Slice the log into 12 equal parts and place into a lightly greased 9 x 12-inch baking pan. Cover pan with plastic wrap and let rolls rest for 30-45 minutes at room temperature. Rolls should rise to the top of the baking pan.
Preheat oven to 350 degrees F. Remove plastic wrap and bake rolls for 30-35 minutes until golden brown on top and the internal temperature of the rolls registers at least 185 degrees F. Allow rolls to cool for 5-10 minute before covering with frosting.
Cream Cheese Frosting: Beat together cream cheese and butter until smooth. Add powdered sugar, cinnamon, and reserved apple filling liquid. Add additional apple liquid, to taste or to achieve desired frosting consistency. Mix until smooth. Spread over warm apple cinnamon rolls.