1. Begin by activating the yeast. In a bowl, combine the warm milk, yeast, and 1 tablespoon of the granulated sugar. Let the mixture sit for 5-10 minutes, or until it becomes foamy and bubbly.

2. Next, add the melted butter, remaining sugar, salt, and eggs to the yeast mixture. Gradually incorporate the all-purpose flour, kneading the dough until it forms a soft, smooth ball. Knead the dough for an additional 6-8 minutes to develop the gluten and create a supple texture. Place the dough in a greased bowl, cover, and let it rise for 1 hour or until doubled in size.

3. While the dough is rising, prepare the apple filling. In a bowl, combine the chopped apples, brown sugar, cinnamon, and nutmeg. Stir to coat the apples evenly.

4. Once the dough has risen, roll it out into a large rectangle. Spread the softened butter evenly over the dough, then sprinkle the apple mixture on top. Carefully roll the dough tightly into a log and cut it into 12 even pieces. Place the shaped rolls in a greased baking dish.

5. Cover the rolls and let them rise for an additional 30 minutes. Preheat your oven to 350°F during this time.

6. Bake the Caramel Apple Cinnamon Rolls for 25-30 minutes, or until they are golden brown and cooked through.

7. While the rolls are baking, whisk together the powdered sugar, milk, and vanilla extract to create a smooth glaze.

8. As soon as the Caramel Apple Cinnamon Rolls come out of the oven, drizzle the warm glaze over the top.