Preheat your oven to 350°F (175°C). This is crucial for ensuring that your cookies bake evenly.
In a large mixing bowl, use an electric mixer to cream together the room temperature unsalted butter, granulated sugar, and light brown sugar until light and fluffy. This should take about 2-3 minutes.
Mix in the creamy peanut butter until fully combined. The mixture should be smooth and cohesive.
Add the eggs one at a time, mixing well after each addition. Then, stir in the pure vanilla extract.
In a separate bowl, whisk together the all-purpose flour, baking soda, and fine sea salt. Gradually add this dry mixture to the wet ingredients, mixing until just combined.
Gently fold in the quick-cooking oats and the entire bag of Reeses Pieces until evenly distributed throughout the dough.
Using a cookie scoop, drop rounded tablespoons of dough onto the prepared baking sheets, leaving enough space between each cookie to allow for spreading. If desired, sprinkle a pinch of flaky sea salt on top of each cookie.
Bake in the preheated oven for 10-12 minutes, or until the edges are golden brown and the centers look slightly undercooked. Remove from the oven and let the cookies cool on the baking sheets for 5 minutes before transferring them to wire racks to cool completely.