Step 1: Reduce the Apple Cider. Place 2 cups of apple cider in a small saucepan over medium-high heat. Simmer until the liquid has reduced to exactly 1/2 cup. This concentrates the apple flavor. Let it cool until it is warm to the touch, but not hot.
Step 2: Bloom the Yeast. In a large bowl or the bowl of a stand mixer, combine the warm milk, 1 tablespoon of the granulated sugar, and the yeast. Let it sit for about 5 to 10 minutes until it becomes foamy and active.
Step 3: Mix the Dough. Add the reduced apple cider, the rest of the granulated sugar, melted butter, egg, salt, and 2 cups of the flour to the yeast mixture. Mix until combined. Gradually add the remaining flour, half a cup at a time, until a soft dough forms and clears the sides of the bowl.
Step 4: Knead the Dough. Knead the dough on a lightly floured surface or with a dough hook for about 5-7 minutes until it is smooth and elastic. Place the dough in a greased bowl, cover with a clean towel, and let it rise in a warm spot for 1 to 1.5 hours or until doubled in size.
Step 5: Prepare the Filling. In a small bowl, whisk together the brown sugar and ground cinnamon until well combined. Ensure your filling butter is softened to room temperature so it spreads easily without tearing the dough.
Step 6: Roll and Fill the Dough. Punch down the risen dough to release air. On a floured surface, roll the dough into a large rectangle (about 12×18 inches). Spread the softened butter evenly across the dough, then sprinkle the cinnamon-sugar mixture over the butter, leaving a small margin at the edges.
Step 7: Shape the Rolls. Starting from the long edge, tightly roll the dough into a log. Use a sharp knife or unflavored dental floss to cut the log into 12 even slices. Place the slices in a greased 9×13 inch baking pan.
Step 8: Second Rise. Cover the pan and let the rolls rise for another 30 to 45 minutes in a warm place until they are puffy and touching each other.
Step 9: Bake the Rolls. Preheat your oven to 350°F (175°C). Bake the rolls for 20 to 25 minutes, or until they are lightly golden brown on top. Avoid overbaking to keep them soft.
Step 10: Glaze and Serve. Whisk together the powdered sugar and the extra apple cider (or milk) until smooth. Drizzle the glaze over the rolls while they are still warm so it seeps into the spirals. Serve immediately.