Preheat oven to 350°F. Line 2 large baking sheets with parchment paper.
Beat butter with both sugars in a large bowl using a wide spatula or hand mixer for 1-2 minutes until smooth and a bit fluffy – it will look like wet sand. Mix in peanut butter. Beat in egg and vanilla until well incorporated. Mix in rolled oats and set aside.
Combine flour, baking soda, baking powder, salt and cinnamon in a medium bowl, then whisk to blend evenly. Add it to the creamed butter mixture and stir it in until mostly combined. Add white chocolate chunks and Reese's pices and fold them through until evenly incorporated.
Roll heaped tablespoons of dough into balls and place them onto prepared baking sheets, spacing them at least 2 inches apart. Flatten each dough ball with the palm of your hand or bottom of a measuring cup and bake for 10-12 minutes until lightly golden around the edges, yet still soft in the center. Let cookies cool for 3 minutes on the baking sheet then transfer individually to a wire rack to finish cooling. Drizzle with melted dark chocolate.