Ready to dive into the baking process? Here’s how you can make these delightful rolls:

1. In a large bowl, combine the flour, sugar, yeast, and salt. Stir in the warm milk, melted butter, and egg. Mix until a dough forms.
2. Transfer the dough to a floured surface and knead for about 8-10 minutes, or until smooth and elastic. Place in a greased bowl, cover, and let rise in a warm place until doubled in size, about 1 hour.
3. While the dough rises, prepare the apple filling. In a medium saucepan, combine the apples, brown sugar, cinnamon, nutmeg, and lemon juice. Cook over medium heat until the apples are soft and the mixture is thick and caramelized, about 10 minutes. Set aside to cool.
4. Once the dough has risen, punch it down and roll it out into a rectangle about 12×18 inches. Spread the softened butter evenly over the dough.
5. Spread the cooled apple mixture over the buttered dough. Carefully roll up the dough, starting from the long side, into a tight log. Cut into 12 even slices.
6. Place the slices in a greased baking dish, cover, and let rise for another 30 minutes while you preheat your oven to 350°F.
7. Bake the rolls for 25-30 minutes, or until golden brown. Remove from the oven and let cool slightly.
8. While the rolls cool, make the icing by whisking together powdered sugar, milk, and vanilla extract. Drizzle over the warm rolls before serving.