Preheat oven to 350°F. Line two baking sheets with parchment.
Put the flour and baking soda in the bowl of a food processor fitted with a metal blade. Pulse to distribute the baking soda evenly. Add the butterscotch chips and process until the chips are ground, with some slightly larger bits remaining. Turn the flour and butterscotch chips out into a large bowl.
In a separate large bowl, use an electric mixer to combine the butter, granulated sugar and brown sugar for 2 to 3 minutes, scraping down the bowl from time to time, until fluffy. Add the egg and pumpkin puree and stir to combine.
Pour the wet mixture into the flour mixture and stir to combine. Add the oats, white chocolate and nuts and stir until the ingredients are combined and no flour is visible. Cover the bowl and refrigerate for at least 10 minutes or overnight.
Use a 3 tablespoon cookie scoop to drop the cookie dough onto the prepared sheets, leaving 2 inches between cookies.
Bake cookies on center rack for 13 to 15 minutes, rotating the cookie sheets halfway through for even baking, until they're light golden brown and no longer doughy looking. Cool cookies on cookie sheets for 10 to 15 minutes before transferring them to a wire rack or clean surface to cool completely.