Preheat your oven to 375 degrees F and line two large baking sheets with parchment paper.
In a stand mixer, combine the butter, light brown sugar, and granulated sugar. Beat until creamy, then add the egg, pumpkin puree, and vanilla extract.
In a separate bowl, whisk together the flour, baking soda, pudding mix, ground cinnamon, pumpkin pie spice, and salt. Gradually mix this into the wet ingredients.
Gently fold in the white chocolate chips until evenly distributed.
Scoop generous portions of dough onto the prepared baking sheets, leaving space between each. Sprinkle the topping mixture over each cookie dough ball.
Bake for about 10 minutes or until the edges are lightly golden brown. Let cool on the baking sheets for a few minutes before transferring to a wire rack.