Heat the water to between 105°F and 115°F. Add a pinch of sugar and the yeast. Stir briefly and then set aside for the yeast to activate, about 5 minutes.
In the bowl of a stand mixer fitted with a dough hook, combine the warm apple cider, melted butter, eggs, sugar, and the yeast mixture. Stir together and then add the flour, cinnamon, and salt.
Mix, using the dough hook, until the dough starts to come together. Scrape down the sides occasionally to encourage the dough to come together. If the dough is too sticky and sticks to the side without forming a ball, then add more flour, a tablespoon at a time.
Continue mixing with a dough hook on low speed for about 5 minutes until the dough is soft and stretchy. After mixing, take the dough out and lightly knead a couple of times on the counter to bring it together into a smooth ball.
Transfer the dough to a greased bowl. Rub a little oil on top of the dough. Cover with cling film or a tea towel and then set in a warm place to rise for 1 to 1 1/2 hours until double in size.
Apple Filling
Start the apple filling right after you make the dough so that it has time to cool down. Melt the butter in a saucepan over medium heat. Add the finely diced apples along with the apple juice and lemon juice and cook until the apples begin to soften, about 3 to 4 minutes.
In a small bowl, combine the brown sugar, cornstarch, cinnamon, and salt. Stir together and ensure there are no lumps.
When the apples are tender but still have a little bite to them, add the sugar mixture and stir together. Cook the apples until the sauce thickens. Remove from the heat and let the filling cool completely.
Cinnamon Filling
In a small bowl, combine the softened butter, brown sugar, and cinnamon. Blend together using a spatula until fully combined.
Assemble the rolls
After the dough has risen, punch it down to deflate completely. Transfer the dough to a lightly floured counter. Roll the dough out into a large rectangle, about 18” by 10” in size. Spread the cinnamon filling over the dough.
Drop the apple filling over the cinnamon filling and gently spread it out evenly. Spray a 9” by 13” baking pan with non-stick spray. Roll the dough up starting with the long side. Use a sharp knife to cut the roll into 12 pieces. Place the rolls in the prepared pan. Cover with a tea towel and let rise for another 30 minutes or until double in size.
Browned Butter Icing
In a small pan or saucepan, melt the butter over medium heat. Let the butter simmer gently until it begins to brown, about 4 to 5 minutes. The butter will foam and then become clear, with the milk solids dropping to the bottom of the pan. Swirl the pan while the butter is cooking to make sure it browns evenly.
When the milk solids begin to turn brown, remove the butter from the heat. Transfer to a bowl and allow to cool. Let the browned butter cool until it is the consistency of softened butter.
In a stand mixer fitted with a paddle attachment, combine the softened browned butter and cream cheese. Beat together until creamy. Add the icing sugar and beat until combined.
Bake the rolls
Preheat the oven to 350°F. Bake the cinnamon rolls for 25 to 35 minutes until lightly browned and cooked through. When the rolls are done, transfer the baking dish to a rack and let sit for a few minutes. Drop the icing onto the warm rolls and let sit for a minute to soften. Gently spread the icing over the rolls. Enjoy!