1. In a large bowl, combine flour, yeast, sugar, and salt.
2. In a small saucepan, heat milk and butter until warm, then stir in eggs.
3. Combine wet and dry ingredients and knead until smooth. Allow dough to rise until doubled, about 1 hour.
4. In a bowl, mix apples, cinnamon, brown sugar, and softened butter.
5. Roll out the dough on a floured surface into a rectangle. Spread apple filling evenly over the dough. Roll tightly and slice into 12 pieces.
6. Place rolls in a greased baking dish, cover, and let rise for another 30 minutes.
7. Preheat oven to 350°F and bake for 25 minutes until golden brown.
8. In a separate bowl, mix frosting ingredients until smooth. Spread over warm rolls.