Preheat the oven to 375 degrees Fahrenheit, with the middle rack in position. Note that this recipe makes enough rolls for two Sweetie Pie dishes.
Make the frosting first: Whisk all ingredients in a mixing bowl on high speed with an eclectic mixer until airy and starting to thicken (about 5 minutes). Place in the fridge to cool; it will continue to thicken.
To make the dough (see the note on flours and substitution at the end):
Have all of your dough ingredients measured out before starting, with dry ingredients in one bowl and wet ingredients in a pourable measuring glass. This method is inspired by King Arthur’s recipe that uses a milk roux/tangzhong. In Saucy, whisk the flour and milk for the roux together over low heat. Whisk until the mixture is thick and coats the bottom of the pot with a thin film when you swipe the bottom with a spatula.
Place the roux in your electric mixer with a dough hook and add your wet and dry ingredients to the bowl. Mix for about 10 minutes on low speed, stopping and removing the dough from the sides and bottom of the bowl with a spatula several times, until smooth and a bit sticky.
Place a loose handful of flour on your work surface before scooping the dough out of the bowl. Use the flour to help you roll the sticky dough into a ball before placing in a bowl. Cover the bowl and place it in a warm part of your kitchen (I like to place it under the stove or oven light with the door open, depending on how hot it gets) and let it double in size for one hour.
Prepare the filling while your dough is proofing. Place all of the filling ingredients in a bowl and work the applesauce through the sugar mixture until everything is evenly distributed and resembles slightly wet sand.
To prepare your apple slices, toss them in the rum and lemon juice until ready to use.
When you are ready to roll your cinnamon rolls, lightly oil or spray the Sweetie Pie dishes, your work surface, and a rolling pin. Roll your dough out into a 14-by-10 rectangle, then spread your sugar mixture on top, leaving a half-inch strip on the top part of the dough empty. Lay your apple slices across the sugar filling. You want to have one layer of apples with some space in between, instead of pieces stacked on top of each other, or it will be difficult to roll.
Next, start to roll your cinnamon rolls. Beginning on one side, roll the dough while working your way across the length of the rectangle. When you reach the other end of the rectangle, roll while working your way back until the dough forms a log and the crease side is on the bottom. From here, slice into 1 1/2inch cinnamon rolls, and place them in Sweetie Pie with a little space in between each for proofing. Cover the dishes before placing them in a warm space to proof again for 20 minutes.
When ready to bake, drizzle the 1/3 cup of heavy cream evenly between both Sweetie Pies and bake in the oven for 18 to 22 minutes. Allow the rolls to cool slightly before glazing and enjoying. You can glaze just the ones you are going to eat immediately and store the glaze in the fridge while the cinnamon rolls remain on your kitchen counter in Sweetie Pie (covered) for several days. Reheat before glazing to enjoy.
Flour substitution notes: I like using Caputo Blue 00 Flour for very soft and airy rolls, but you can substitute AP flour or bread flour if that is what you have on hand. If you would like to make this recipe gluten-free, you need gluten-free breadcrumbs for the filling and a gluten-free flour. I recommend following the instructions on the flour packaging for substitution, as you may need additional flour to make sure the dough will be able to roll.
Dairy substitution notes: If you would like to substitute dairy in this recipe, you can swap out the whole milk and heavy cream for a nut milk (almond, cashew, or preferably walnut would work well here). For the frosting, you would substitute 1 cup of nut milk for the quark, and add the juice of half a lemon and 1 tablespoon of cornstarch to the recipe. You would then need to heat the mixture in a pot over a low heat, whisking until thickened and then cooled.