1cup(212g)lightly packed brown sugar, more or less depending on sweetness of apples
1 ½teaspoonsground cinnamon
1 ½cups(171g)powdered sugar
¼cupmilk or cream
For the dough, heat the milk in a medium saucepan until the milk is scalded (which is basically heating it until right before it simmers - it will start steaming and little bubbles will form around the edge of the pan). Pour the milk into the bowl of an electric stand mixer fitted with the dough hook (or you can do this by hand with a large bowl, wooden spoon and lots of elbow grease).
Add the butter, sugar and salt. Mix until the butter is melted and let the mixture cool until warm but not hot.
Add the yeast and eggs and mix until combined.
Gradually add the flour until the dough clears the sides of the bowl. The exact amount will depend on the temperature, humidity and how you measure flour. The dough should be pretty soft and just slightly sticky without leaving a lot of residue on your fingers - don't overflour until the dough is stiff or else the rolls will be dry. Let the dough knead for 1-2 minutes.
Transfer the dough to a large, lightly greased bowl. Cover with lightly greased plastic wrap and let it rise until doubled.
While the dough rises, make the filling by melting the 3 tablespoons butter in a large nonstick skillet over medium heat. Add the apples and salt and cook for 3-4 minutes until the apples soften slightly. Add the brown sugar, cinnamon and flour and stir to coat the apples with the mixture. Continue cooking over medium heat, stirring often, until the mixture is thick and syrupy and the apples are cooked and tender. Remove from the heat to cool completely (you can speed up this process by scraping the mixture into a bowl and refrigerating).
Line a large rimmed baking sheet (about 11X17-inches) with parchment paper. Set aside.
Lightly punch down the dough and on a lightly greased countertop, press it into about an 18X12-inch rectangle.
Spread the cooled apple mixture over the dough leaving a 1/2-inch border at one long edge. Start rolling from the other long edge. This part is a little messy. Don't let it stress you out (you know, like it did me). It's ok if the filling spreads and squeezes out a bit. It helps to kind of lift the dough up as you roll it - lifting it over the filling instead of smushing it out if that makes sense - these won't roll up as nice and tight as a classic cinnamon roll. Once rolled up, pinch the edge to seal.
Using unflavored dental floss or a sharp serrated knife, cut the long roll into 12-15 rolls and space evenly on the prepared baking sheet about an inch or so apart (if you only cut 12 rolls, still space them somewhat close together even if it leaves an empty space at the end of the pan - you don't want them too far apart). It's ok if the filling oozes out as you cut; you can scrape up any excess filling and drizzle it over the rolls once they are on the pan. Cover with lightly greased plastic wrap and let rise until puffy and nearly doubled, about 45 minutes to an hour (maybe longer if your kitchen is cool).
Preheat the oven to 350 degrees, uncovered the rolls and bake for 20-25 minutes until just lightly golden on top and around the edges.
For the glaze, whisk together the powdered sugar, milk or cream, and vanilla until smooth. Let the rolls cool until just warm before drizzling with the glaze.
These rolls are best served warm, in my opinion. They reheat really well for just a few seconds in the microwave.
Yeast: if you don't have instant yeast and want to use active dry, dissolve the yeast in a couple tablespoons warm water with a pinch of sugar. Apple Mixture: it's really important to let the apple mixture cool to room temperature (chilled is even better). It's a bit of a messy process rolling it up in the dough - but is much better if the mixture is cooled and not overly warm.Milk: I have best results using 2% or whole milk for this recipe.Make-Ahead:this post details how to make sweet rolls ahead of time.