Preheat the oven to 375 degrees F.
Combine the brown sugar, butter and oil in the bowl of a stand mixer and mix on high speed, stopping occasionally to scrape down the bowl, until the mixture is light and fluffy, about 2 minutes. Add the applesauce, vanilla and egg white and mix to combine. Add the flour, oatmeal, cinnamon and salt and mix just until just combined. Add the apricots, cherries, walnuts and chocolate and mix to combine.
Spray a baking sheet with nonstick cooking spray. Using 1 tablespoon of cookie dough at a time, roll into balls and place 2 inches apart on the baking sheet. Press the balls down with the palm of your hand to flatten slightly, as the cookies will not spread as much as cookies with more butter. Bake until lightly browned but still soft, 12 to 14 minutes. Remove from the oven and cool on racks.
From Food Network Kitchens; after further testing and to ensure the best results this recipe has been altered from what was in the actual episode.