Melt butter in a large skillet over medium heat. Add apples and salt and cook until slightly softened, about 3 to 5 minutes. Stir in brown sugar, all-purpose flour, and cinnamon, and continue cooking, stirring often, until the apples are cooked through and the mixture is thick, about 5 minutes. Remove from the heat and set aside to cool completely before using.

In a small saucepan combine milk, butter, and sugar and cook over medium low heat until lukewarm. The butter will not be completely melted, but should be lukewarm. If it is too hot it will kill the yeast, so wait a few minutes until it cools down before proceeding.

In the bowl of a stand mixer fitted with a dough hook, mix together all-purpose flour, yeast, and salt. With the machine running on low, add eggs and milk mixture. Knead on low speed until all of the dough comes together, then increase the speed to medium and knead until the dough is smooth and elastix, about 10 minutes. Transfer the dough to a lightly greased bowl, cover, and allow it to double in size, about 1 hour.

Set aside a parchment lined 9-inch round baking pan.

Preheat oven to 350°F.

After the dough has doubled in size, punch it down and transfer to a lightly floured surface. Roll the dough out into a large rectangle, about 12”x14”. Spread the prepared filling evenly over the surface, leaving a ½-inch border along the edges.

Starting with the longer side, gently roll into a log. Lightly pinch the seams together. Using a sharp knife or unflavored dental floss, trim and discard the edges, then gently slice into 8 segments. Place the rolls cut-side up in the prepared pans. Cover and allow them to rise until nearly doubled, about 45 to 60 minutes.

Remove from the oven and cool slightly before glazing.

In a small bowl, whisk together all ingredients until smooth. Drizzle over slightly cooled rolls.