Prepare the dough: In a bowl, mix flour, yeast, sugar, and salt. Add warm milk, melted butter, and egg. Knead until smooth and elastic. Cover and let rise 1–1.5 hours, until doubled.
Prepare the filling: In a small bowl, combine apples, brown sugar, cinnamon, and softened butter.
Roll and fill: Roll the dough into a rectangle, about 12×8 inches. Spread the apple mixture evenly over the dough.
Shape the rolls: Roll the dough tightly into a log and cut into 8–10 slices. Place rolls in a greased baking dish. Cover and let rise 30–45 minutes.
Bake: Preheat oven to 350°F (175°C). Bake rolls for 25–30 minutes until golden brown.
Prepare the icing: Mix powdered sugar, milk, and vanilla until smooth. Drizzle over warm rolls.
Serving and Storage Tips
