1. Make the Dough:

1. In a large mixing bowl, combine 2 ¼ cups of flour, sugar, yeast, and salt. Stir to combine.
2. Add the warm milk, melted butter, and egg. Mix until well combined.
3. Gradually add the remaining flour, ¼ cup at a time, until a soft dough forms.
4. Knead the dough on a lightly floured surface for about 5-7 minutes, until it becomes smooth and elastic.
5. Place the dough in a greased bowl, cover it with a damp cloth, and let it rise in a warm place for 1 hour, or until it doubles in size.

2. Prepare the Apple Filling:

1. In a medium saucepan, melt the butter over medium heat.
2. Add the diced apples, brown sugar, cinnamon, and nutmeg. Cook for 5-7 minutes until the apples are tender and the sugar has dissolved.
3. Stir in the flour and cook for an additional 1-2 minutes to thicken the mixture.
4. Remove from heat and let cool slightly.

3. Assemble the Rolls:

1. Punch down the risen dough and roll it out on a lightly floured surface into a 12×18 inch rectangle.
2. Spread the apple filling evenly over the dough, leaving a ½-inch border around the edges.
3. Starting from the long side, tightly roll the dough into a log.
4. Cut the log into 12 equal slices and place them cut side up in a greased 9×13 inch baking dish.
5. Cover the dish with a damp cloth and let the rolls rise for 45 minutes, or until they have doubled in size.

4. Bake the Rolls:

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

5. Make the Cream Cheese Glaze:

1. In a medium bowl, beat the cream cheese and butter together until smooth and creamy.
2. Add the powdered sugar and vanilla extract, and beat until fully combined.
3. Gradually add the milk until the glaze reaches your desired consistency.

6. Glaze and Serve:

1. Once the rolls are out of the oven, let them cool slightly before drizzling the cream cheese glaze over the top.
2. Serve warm and enjoy!