In a large liquid measuring cup, whisk together the milk and instant yeast, followed by the eggs.
In the bowl of a stand mixer, whisk together the flour, cornstarch, sugar and salt. Attach the dough hook, turn the mixer on low speed and add the warm milk mixture followed by the apple cider. Allow the ingredients to combine for one minute. Increase the speed to medium and add the butter in pieces until it's all incorporated. The dough will be very wet. Allow it to continue mixing for 5 minutes. The dough should be very soft and delicate but not too sticky to handle. Transfer the dough to a lightly greased large bowl and cover with a clean kitchen towel. Allow the dough to double in size, up to 2 hours.
While the dough is rising, prepare the filling. Combine the brown sugar, cinnamon and salt in a bowl. Grease 2 8-inch cake pans thoroughly and set aside.
Place the dough on a lightly floured countertop. Roll the dough into a large, thin rectangle, approximately 19 x 14 inches. Using clean hands, spread the butter across the dough, leaving a small border around the edges, and then top evenly with the brown sugar mixture. Sprinkle the chopped apples on top of the sugar.
Roll the dough into a tight cylinder. Cut into16 even pieces and place in the reserved cake pans, cut side up. Cover and allow to double in size, approximately 1 hour.
Prepare the glaze by whisking together the confectioners' sugar, creme fraiche (or cream cheese), and apple cider. Set aside.
Bake the buns at 350 degrees F for 30-35 minutes, or until the tops are golden brown. Top each pan with 1/4 cup of the glaze and allow the buns to cool completely. Top with the remaining glaze before serving.
Notes
Either sweet or tart apples will work in this recipe, but tart apples will offer more of a flavor balance. Remove the buns from the cake pans before refrigerating.You can do most of the prep work the day before, then bake them in the morning. At step 5: After placing the buns in the prepared cake pans, immediately cover and chill. The next day, let the dough come to room temperature, then continue with the recipe. This will add an extra 30-45 minutes or so to the rise time.I prefer using creme fraiche in the glaze. It's slightly thinner and has a more complex flavor. But cream cheese is more traditional and will work perfectly well! Sour cream would also work.