In a medium mixing bowl whisk together the flour, baking soda, cinnamon and salt. Set aside.
In the bowl of an electric mixer beat together the butter and sugars on medium speed until light and fluffy (at least 3-4 minutes). Add the eggs, one at a time, mixing after each addition. Add the apple sauce and vanilla and beat on medium-high for 1 minute.
Turn mixer to low and carefully add flour. Mix until just combined (no over-mixing here). Using a rubber spatula, gently stir in the oats. Fold in the cooled caramelized apples, mixing until just combined. Cover mixing bowl with plastic wrap or a piece of foil and refrigerate for at least 2 hours.
When ready to bake, preheat oven to 375 degrees F and line a baking sheet with parchment paper.
Use a medium cookie scoop to scoop dough onto baking sheet, placing each cookie at least 1-2" apart, as they will flatten out while baking. Bake cookies for 15-18 minutes, or until edges are just starting to brown, but the middle is still a little soft.
Remove baking sheet from the oven and allow cookies to cool for at least 5 minutes before transferring to a cooling rack to cool completely. Repeat process until all cookies have been baked.
Allow cookies to cool completely before drizzling with the sugar glaze (see below).