Grease a large bowl and set aside. In the bowl of a stand mixer fitted with a paddle, combine the apple cider, granulated sugar, and yeast, and let sit until the yeast has dissolved, about 5 minutes.

Add the eggs and salt to the yeast mixture and mix on low until well combined.

Add the flour, mixing on low speed until incorporated, about 1 to 2 minutes.

Add the butter, one piece at a time, mixing until completely incorporated after each addition.

Increase the speed to medium and beat the butter into the dough until all the butter pieces are incorporated, about 1 minute.

Transfer the dough to the prepared bowl. Cover the bowl with plastic wrap and let the dough rise for 30 minutes.

Remove the plastic wrap and fold the dough over itself several times, giving the bowl a quarter turn after each fold. Cover the bowl again and let the dough rise for another 30 minutes.

Repeat the folding and rising process three more times for a total rise time of 2 hours.

Tightly cover the bowl with plastic wrap and refrigerate overnight or for up to 72 hours.

In a small bowl, mix together the granulated sugar, cinnamon, and salt for the filling.

Grease and line a Pullman pan with a parchment sling. Lightly flour your work surface and roll the dough into a 20 by 12 in rectangle.

Brush the dough with melted butter and sprinkle the cinnamon-sugar mixture over the dough, pressing it into the dough.

Cut the dough crosswise into five strips, each about 12 by 4 in, then stack the strips.

Slice the stacked strips into six equal strips, each about 4 by 2 in. Fit the strips into the prepared loaf pan, cut edges up and side by side.

Cover the pan with plastic wrap and let the dough rise in a warm place until almost doubled in size, about 45 to 60 minutes.

Preheat the oven to 350F. Place a sheet pan on a lower rack to catch drips.

Bake the bread until golden brown, about 40 to 50 minutes or until it registers 200F.

In a medium saucepan, cook the apple cider and salt over medium-high until reduced to ? cup, about 3 to 4 minutes. Remove from heat and whisk in the cream cheese, butter, vanilla, and optional apple brandy until smooth.

Slowly add the confectioners? sugar to the apple cider mixture, whisking constantly until smooth and glossy.

Transfer the loaf pan to a wire rack and pour half of the icing over the bread. Let sit for 15 minutes.

Use a sling to gently remove the loaf from the pan, then drizzle remaining icing over the loaf. Let cool slightly before serving.