Line an 8x8inch glass or ceramic baking dish or metal baking pan with parchment (see the tutorial on page 000).
In a small bowl, whisk together 1 cup of the flour, yeast, and salt. Set aside.
In a large microwave-safe bowl, heat the milk, cider, and butter on high for 60 to 90 seconds, until the butter is melted. Allow the mixture to cool to 120°F.* Mix in the sugar and egg. Mix in the flour mixture, then add enough of the remaining flour so it’s easy to handle (e.g., not too sticky). Depending on the humidity in the room, you may or may not need all of the remaining flour.
Transfer the dough to a lightly floured surface and knead it for about 5 minutes. A good way to tell if you’re done kneading is to poke your finger into the dough—if the indentation pops right back out it’s ready. Let the dough rest for 10 minutes.
On a lightly floured surface, roll out the dough into a 9x9inch square. Brush the butter for the filling all over the surface of the dough. In a small bowl, combine the sugars and cinnamon; sprinkle them over the butter. Scatter the apples and walnuts on top. Carefully and tightly roll up the dough. Slice the dough into 9 equal pieces (about 1inch wide each), and arrange them, cut side down, in the prepared dish or pan. Leave space between each roll—they will rise and expand. Cover the dish or pan with plastic wrap and set in the refrigerator overnight, or for at least 8 hours.
Uncover the dish or pan and set it out at room temperature an hour before you’re ready to bake
the rolls.
Heat the oven to 350°F for glass or ceramic dishes or 375°F for metal pans.
Bake until the rolls are lightly browned and a thermometer inserted in the center reads 190°F, about 25 minutes. If the rolls begin browning too fast, you can cover them lightly with foil.
To make the glaze, bring the cider, cinnamon, and salt to a boil in a small saucepan over medium heat. Lower the heat and simmer until the cider is reduced to 2 tablespoons, 4 to 5 minutes. Remove the saucepan from the heat and stir in the butter and confectioners sugar. Drizzle the glaze over the rolls right before serving.
*Yes, you need to use a thermometer for this—if the liquids are too hot they may kill the yeast.