Grease a large bowl.

In a large liquid measuring cup, combine the eggs, apple cider, and honey.

In the bowl of a stand mixer fitted with a paddle, mix the flour, yeast, and salt and stir on low to combine. Add the egg mixture and mix on low to combine. With the mixer on low, add the butter, one piece at a time. When all the butter has been added, increase the speed to medium and beat the butter into the dough, until all the little butter pieces are incorporated, 1 minute. Transfer the dough to the prepared bowl. The dough will be very sticky and you will need a spatula to scrape the dough into the bowl.

Cover the bowl with plastic wrap and let rise for 30 minutes. Place your fingers or a spatula underneath the dough and gently pull the dough up and fold it back over itself. Turn the bowl and repeat this folding again. Continue 6 to 8 more times, until all the dough has been folded over on itself. Re-cover the bowl with plastic and let rise for 30 minutes. Repeat this series of folding 3 more times, for a rise time of 2 hours and a total of 4 foldings. Tightly cover the bowl with plastic wrap and refrigerate overnight or up to 72 hours.

Flour a work surface and knead the Sweet Dough 10 to 12 times. Shape the dough into a ball, cover the top lightly with flour, then cover with a tea towel and let come to room temperature.

Grease a 9×13-inch pan; if desired, line with parchment paper (this makes for easier cleanup).

In a small bowl, mix the brown sugar, cinnamon, spices, and salt.

Roll the dough into a 16 by 12-inch rectangle. Brush the dough with the melted butter and sprinkle the sugar-spice mixture evenly over the top, pressing it lightly into the butter so it adheres. Starting at a long side, roll the dough into a tight cylinder. Pinch the seam gently to seal it and position the dough seam side down. Use scissors or a sharp knife to cut the dough into 12 equal pieces. Transfer the pieces to the prepared pan and place them cut side up. Cover the pan loosely with plastic wrap and let the dough rise until doubled, 1 to 1 1/2 hours.

Adjust an oven rack to the middle position. Preheat the oven to 350 degrees F (180C). Remove the plastic and bake 27 to 32 minutes, rotating the pan halfway through, until the rolls are golden brown. While the rolls are baking, prepare the icing.

Transfer the pan to a wire rack and let cool for 5 minutes. Using an offset spatula or table knife, apply a thin layer of the icing, using about one-third of the mixture. Let the apple cider cinnamon rolls cool for another 15 to 20 minutes. Top with the rest of the icing and serve.

In a medium saucepan, cook the apple cider and salt over medium-high until reduced to 1/4 cup, 3 to 4 minutes. Remove from the heat, and whisk in the cream cheese, butter, and vanilla, and whisk until smooth (there may be a few tiny cream cheese lumps, but they will come out as you whisk in the confectioners’ sugar). Slowly add the powdered sugar to the apple cider mixture, whisking constantly, until the mixture is smooth and glossy.