Step 1: Line a baking sheet with parchment paper or wax paper. Set aside.
Step 2: In a large saucepan, combine granulated sugar, butter, and milk. Bring the mixture to a rolling boil over medium heat, stirring constantly.
Step 3: Once a rolling boil is reached, continue to boil for exactly 1 minute without stirring. Remove the saucepan from the heat immediately.
Step 4: Stir in the pumpkin puree, pumpkin pie spice, vanilla extract, and salt until well combined.
Step 5: Quickly add the old-fashioned rolled oats and optional peanut butter (if using), stirring until everything is thoroughly incorporated and coated. If adding nuts, stir them in now.
Step 6: Working quickly, drop spoonfuls of the cookie mixture onto the prepared baking sheet. You can use a cookie scoop for uniform size.
Step 7: Allow the cookies to cool and set completely at room temperature for about 1 hour, or place them in the refrigerator for 30-45 minutes to speed up the setting process. Once firm, they are ready to enjoy!