Warm milk to body temperature, then mix with active dry yeast and brown sugar. Let sit for 5-10 minutes until bubbly.

Add softened unsalted butter, eggs, and most of the all-purpose flour along with salt. Mix until combined, then knead on a floured surface for about 8-10 minutes.

Place kneaded dough in a greased bowl, cover, and allow to rise in a warm place until doubled, about 1 hour.

Punch down the dough gently, roll it out into a rectangle about ¼ inch thick, and spread melted butter over it.

Mix brown sugar and cinnamon, sprinkle over the dough, then add apple pieces. Roll tightly into a log and slice into 12-15 pieces.

Arrange sliced rolls in a greased baking dish, cover, and let rise again for about 20-30 minutes.

Preheat oven to 350°F (175°C) and bake rolls for 25-30 minutes until golden brown.

While baking, prepare icing by browning unsalted butter, letting it cool slightly, then mixing with cream cheese, maple syrup, powdered sugar, vanilla, and salt.

Once rolls are baked, drizzle with icing and serve warm.