• Combine 2 cups flour, sugar, dry yeast and salt in a large mixer bowl and stir until blended.
• Place water and butter in a microwave-safe bowl. Microwave on HIGH in 15 second increments until very warm but not hot to the touch. (Butter won’t melt completely)
• Add to flour mixture with the egg.
• Beat 2 minutes at medium speed , scraping bowl occasionally.
• Add 1 cup flour and beat 2 minutes at high speed, scraping bowl occasionally.
• Stir in just enough remaining flour so that the dough forms into a ball.
• Kneed on lightly floured surface until smooth and elastic and dough springs back when lightly pressed with 2 fingers, about 6 to 8 minutes.
• Cover with a towel; let rise for 10 minutes.

For the apple filling

• Add all of the filling ingredients into skillet and cook at medium heat until apples are thick and sauce gets thick, about 10 minutes.
• After dough has risen for 10 minutes roll into a 15×10 inch rectangle using a rolling pin
• Spread 3 tablespoons of butter over dough stopping at least 1/2 inch from the edges of on the long sides.
• In a small bowl combine 1/3 c sugar and 2 tsp ground cinnamon.
• Sprinkle mixture on top of rolled out dough.
• Add cooked apple mixture on top. Use a slotted spoon to spoon the apples onto the dough. This will get rid of some of the extra liquid.
• Starting at the long end of the rectangle, roll up tightly. Pinch seams to seal. Some of the filling might ooze out. This is ok. You can spoon the filling that oozed out over the top of the rolls once you have cut them and put them in the pan.
• Cut into 12 equal pieces.
• Place, cut sides down, in greased 13×9 inch baking pan.
• Cover with towel; let rise in warm place until doubled in size, about 1 hour.
• Bake in preheated 350 F oven for 25 to 30 minutes or until rolls are golden brown.
• Cool on wire rack for at least 20 minutes.
• Combine all frosting ingredients and mix until smooth and creamy.
• Add more milk if you need to get a drizzle consistency.
• Drizzle over rolls.