Preheat your oven to 350°F (175°C). This ensures that your cookies bake evenly and rise perfectly.
In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until smooth and fluffy. This should take about 2-3 minutes with an electric mixer on medium speed.
Mix in the applesauce (or single serve package) until well combined. Then, add the eggs one at a time, mixing well after each addition. Finally, stir in the vanilla extract.
In a separate bowl, whisk together the butterscotch pudding mix, baking soda, and flour. Gradually add this dry mixture to the wet ingredients, mixing until just combined. Be careful not to overmix.
Using a spatula, gently fold in the chopped mini Reese's Peanut Butter Cups until evenly distributed throughout the cookie dough.
Using a cookie scoop or tablespoon, drop rounded balls of dough onto the prepared baking sheet, leaving enough space between each cookie to allow for spreading. Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden.
Once baked, let the cookies cool on the baking sheet for about 5 minutes before transferring them to a cooling rack. Allow them to cool completely before indulging (if you can resist!).