1. Make the Dough:

1. In a large bowl, combine the warm milk, yeast, and granulated sugar. Let sit for 5-10 minutes, or until the mixture becomes frothy.
2. Add the melted butter, egg, salt, and 3 cups of the flour. Mix until a soft dough forms. Gradually add the remaining 1/2 cup of flour as needed.
3. Knead the dough on a floured surface for 6-8 minutes, or until smooth and elastic. Alternatively, use a stand mixer with a dough hook.
4. Place the dough in a greased bowl, cover with a clean towel, and let rise in a warm place for 1 hour, or until doubled in size.

2. Prepare the Filling:

1. In a medium bowl, mix the granulated sugar, brown sugar, and cinnamon.
2. Dice the apples into small pieces.

3. Assemble the Rolls:

1. Punch down the risen dough and roll it out into a 12×18-inch rectangle on a floured surface.
2. Spread the softened butter evenly over the dough.
3. Sprinkle the cinnamon-sugar mixture over the butter, then evenly distribute the diced apples on top.
4. Starting from the long edge, roll the dough tightly into a log. Slice into 12 even rolls and place them in a greased 9×13-inch baking dish.

4. Second Rise:

1. Cover the rolls with a towel and let rise for 30 minutes, or until puffy.

5. Bake:

1. Preheat your oven to 350°F (175°C).
2. Bake the rolls for 25-30 minutes, or until golden brown and cooked through.

6. Make the Caramel Sauce:

1. In a small saucepan, melt the butter over medium heat. Add the brown sugar and stir until dissolved.
2. Slowly stir in the heavy cream and salt, and simmer for 2-3 minutes until the sauce thickens slightly. Remove from heat.

7. Glaze the Rolls:

1. Drizzle the warm caramel sauce over the baked rolls. For extra indulgence, serve with additional caramel sauce on the side.