Pre-heat oven to 350 degrees F (180 C). Cream butter and sugars together in bowl of stand mixer (or with hand mixer). Scrape sides of bowl and add coconut cream and applesauce; beat until well combined. Add vanilla, soda, and salt. Add flour one cup at a time and beat after each addition but just until combined. (If you are using a hand mixer you may have to hand stir the last cup of flour into the dough.) Stir in chocolate and line a cookie sheet with parchment.
Roll the dough into balls, about 1 1/2 tablespoons each, and place about 2 inches apart on baking sheet. Now take each dough ball and flatten into a disk, then place a peppermint patty in the center and gently shape dough around it and roll between your palms. Place cookies back on tray, top with some extra chocolate chunks if desired, then push them down slightly and repeat with all the cookies.
Bake for 8 - 10 minutes until edges just start to turn golden brown. Remove from oven and cool for about 5 minutes before moving to cooling rack.
Recipe Notes
If you have trouble finding coconut cream at your local grocery store it's completely fine to use full-fat coconut milk and scrape the cream off of the top. Just be sure that it's cold enough to separate.