Warm the milk and water together until warm but not hot. Stir in the yeast and about 1 teaspoon of the sugar. Let sit for about 5 minutes, until the yeast becomes foamy.
Step 2: Make the Dough
Add the remaining sugar, egg, melted butter, salt, and 4 cups of flour. Mix until a dough forms, adding a little more flour only if needed. Knead the dough for about 8 minutes, until smooth and elastic.
Step 3: Let the Dough Rise
Place the dough in a greased bowl, cover, and let rise in a warm place for about 1 hour, or until doubled in size.
Step 4: Prepare the Apple Pie Filling
While the dough rises, add the diced apples, butter, brown sugar, and apple pie spice to a saucepan. Cook over medium heat for 5–7 minutes, stirring occasionally, until the apples begin to soften. Stir in up to 2 tablespoons of flour and continue cooking for another 3–5 minutes, until thickened. If it becomes too thick, add a small splash of water or apple juice. Set aside to cool.
Step 5: Make the Cinnamon Roll Filling
Mix the softened butter, brown sugar, and apple pie spice together until well combined and spreadable.
Step 6: Roll Out the Dough
Once the dough has doubled, roll it into a rectangle about 12 × 18 inches.
Step 7: Add the Filling
Spread the butter, brown sugar, and spice mixture evenly over the dough. Dollop about two-thirds of the cooled apple pie filling over the top, leaving the remaining third for topping, and spread it evenly across the dough.
Step 8: Cut the Rolls
Using a pizza cutter, cut the dough into 12 strips along the long side of the rectangle.
Step 9: Shape and Arrange the Rolls
Roll each strip into a spiral and place the rolls into buttered baking pans. I like to place 8 rolls in a 9 × 13-inch pan and 4 in an 8-inch pie plate so they aren’t overcrowded.
Step 10: Let the Rolls Rise Again
Cover the rolls and let them rise for about 30 minutes.
Step 11: Bake the Rolls
Bake at 350°F for about 25 minutes, or until the rolls are lightly golden and the centers reach about 190°F.
Step 12: Make the Icing
While the rolls cool slightly, beat together the butter, powdered sugar, maple syrup, and vanilla until smooth and creamy.
Step 13: Ice and Finish the Rolls
Spread the icing over the warm rolls and finish with spoonfuls of the remaining apple pie filling.
Step 14: Serve Warm
Serve the rolls warm and enjoy.