In a large mixing bowl, combine the first five scone ingredients and then mix in the butter pieces just until the mixture is crumbly - you will see some larger butter pieces, which is okay. Stir in the grated apple.
In another bowl combine eggs, vanilla, and applesauce. Add to the dry ingredients and mix just until all the flour is incorporated.
Line a large baking sheet with parchment or silicone liner (or ungreased pan), sprinkle some flour over the center and scrape the dough on top. Pat into a rough circle and divide in half (if it's sticky, sprinkle with a bit of flour). Gently shape each circle into a 5"- 6" round, flouring hands as needed. Use a knife to cut each round into six pieces, flouring knife before each cut.
Brush the cut rounds with milk (and sprinkle with a mixture of cinnamon and sugar if you're not making the caramel glaze). Place the baking sheet into the freezer, uncovered, for 25 to 30 minutes.
Preheat oven to 425 degrees while scones are in the freezer.
Bake for 18 to 20 minutes, until golden brown (make sure they are baked in the middle - if unsure, pull a section apart to see the center).
Transfer scones to a rack over a piece of wax paper or another cookie sheet (to catch any caramel drips) and let cool a bit.
For the caramel glaze:
While the scones are baking, combine butter, brown sugar, and milk or cream in a medium saucepan and bring to a low boil.
Boil for 2 minutes, stirring constantly, and remove from heat. Set aside to until scones are baked and have cooled 5 to 10 minutes.
Use a spoon to drizzle the glaze over the scones and the back of the spoon to spread evenly, as desired.
Any leftover caramel glaze can be refrigerated for a couple of weeks and reheated to soften as needed for, oh, any number of things...caramel lattes, maybe? In fact, you may want to double the recipe just to have some left!