Begin by gently warming 1 cup of milk to 110°F (45°C) and pour it into a mixing bowl. Add 2 1/4 teaspoons of active dry yeast and 1 tablespoon of granulated sugar, stirring lightly. Let this mixture sit for about 5 minutes until it becomes frothy.

In the same bowl with the yeast mixture, add 1/3 cup of granulated sugar, 1/2 cup of melted unsalted butter, 1 teaspoon of salt, and 2 large eggs. Stir until just combined. Gradually incorporate 3 cups of all-purpose flour, mixing until the dough begins to pull away from the sides of the bowl.

Transfer your dough onto a floured surface and knead for 5 to 7 minutes until it becomes smooth and elastic. Once kneaded, place it in a greased bowl, cover with a damp cloth, and let rise in a warm area for 1 to 2 hours or until it's doubled in size.

While the dough rises, prepare the filling. In a separate bowl, mix 1/2 cup of light brown sugar, 2 tablespoons of ground cinnamon, 1/2 teaspoon of nutmeg, and a pinch of salt.

Once your dough has risen, punch it down gently and roll it out on a floured surface into a rectangle about 1/4-inch thick. Spread 1/2 cup of softened unsalted butter evenly over the surface. Sprinkle the filling mixture generously over the buttered dough, followed by the 2 large chopped apples.

Starting from the long edge, carefully roll the dough into a tight log. Pinch the seams to seal it well. Cut the log into 12 to 14 equal slices and place the slices in a greased baking pan, ensuring they are close but not touching. Let them rise for another 30 minutes.

Preheat your oven to 350°F (175°C) during the last 10 minutes of the second rise. Bake the Caramel Apple Cinnamon Rolls for 25 to 30 minutes, or until they’re golden brown and puffed up.

While the rolls are baking, prepare the caramel glaze. In a saucepan, combine 1/2 cup of melted butter and 1/2 cup of light brown sugar over medium heat. Stir until the sugar dissolves, then add 1/4 cup of milk and increase the heat until it comes to a gentle boil. Remove from heat and whisk in 2 to 3 cups of powdered sugar until smooth.

Once the rolls are out of the oven, allow them to cool slightly for about 10 minutes. Drizzle the warm caramel glaze generously over the top of the rolls.