In a medium saucepan, melt the unsalted butter over medium-low heat. Once melted, remove from heat. Stir in the brown sugar and granulated sugar. Continue stirring for 2-3 minutes until the mixture becomes silky smooth and glossy. Let the mixture cool for 5-10 minutes before proceeding.
Once the butter-sugar mixture has cooled slightly, stir in the vanilla extract and large egg yolk until fully combined. Next, add the pure pumpkin and mix until the batter is smooth and cohesive.
Add the all-purpose flour, old-fashioned oats, baking soda, salt, pumpkin pie spice blend, and ground cinnamon to the bowl with the wet mixture. Stir well, making sure all ingredients are fully incorporated and no dry streaks remain. I like to use a spatula or wooden spoon for even mixing at this stage.
Cover the cookie dough and chill it in the refrigerator for 15 minutes to help firm it up. Meanwhile, preheat your oven to 350°F (175°C). Once the dough has chilled, fold in the white chocolate chips until evenly distributed throughout.
Using a cookie scoop or two spoons, drop mounds of cookie dough onto baking sheets lined with parchment paper or a Silpat. Bake in the preheated oven for 10-13 minutes, or until the cookies are lightly golden brown on the edges. Let the cookies set up for 5-10 minutes on the pan before transferring them to a cooling rack. I find letting them cool slightly on the pan helps them hold together and gives a nice chewy texture.