Dough

1. In a small bowl or measuring cup, combine 3/4 cup warm milk and yeast. Let stand for 5-10 minutes until yeast is foamy and activated.
2. Using the paddle attachment in a stand mixer, mix together the melted butter, sugar, sour cream, egg and remaining 1/4 cup of milk on a low speed.
3. In a large bowl, whisk together 3 2/3 cups flour and salt. Add half of the flour mixture to the butter mixture and stir on low speed. Add in yeast mixture and mix until just combined. Mix in remaining flour mixture. Switch to the dough hook attachment. Beat at medium speed until the dough is smooth, elastic and pulls away from the sides of the bowl. If needed, add in remaining 1/3 cup flour (the dough should not be sticky).
4. Grease a large bowl with cooking spray and place dough in the bowl, turning to grease the top. Cover with plastic wrap or a clean kitchen towel and let rise in a warm, draft free place until doubled in size, about 1 hour.

Assembly

1. Spray a 13×9 inch baking dish or sheet pan with cooking spray.
2. Lightly punch down the risen dough and then turn out onto a floured work surface. Roll dough into an 18×12 inch rectangle.
3. Spread softened butter evenly over the dough, leaving a 1/2 inch border on the farthest long edge. Next, evenly spread on the apple butter. Sprinkle on the brown sugar and cinnamon. Finally, add diced apples on top of the dough. Brush the beaten egg over the long edge of dough without any filling.
4. Start with the long side closest to you, begin rolling the dough into a log, pinching the seam to seal. Trim off both ends of the dough. Using a serrated knife or unflavored dental floss, cut the dough into 12 equal sections. Place in the prepared pan. Cover, and let rise until rolls are puffed, about 30 minutes.
5. Preheat oven to 350°F. Bake 25-30 minutes, until rolls are golden brown and cooked through. Let cool for about 10 minutes while you prepare the frosting.

Frosting

1. In a stand mixture with the paddle attachment, beat the cream cheese and butter together until well combined and creamy. Gradually add in the powdered sugar and beat until fluffy. Stir in the caramel sauce. If frosting is too thick add in the milk.
2. Spread onto warm breakfast rolls.