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