Preheat your oven to 350°F (175°C). Grease the bottom and sides of a 13×9-inch baking pan.
In a large bowl, combine the cake mix, vegetable oil, eggs, sour cream, pumpkin, and pumpkin pie spice. Beat with an electric mixer on medium speed for about 2 minutes until the ingredients are just incorporated. Measure out 2 cups of the batter and spread it evenly over the bottom of your prepared pan.
In a small bowl, combine the chopped walnuts with the brown sugar. Sprinkle this mixture evenly over the cake batter in the pan.
Spoon the remaining batter evenly over the filling. Use a spatula to carefully spread the batter to the edges of the pan, covering the filling completely.
Bake in the preheated oven for 35-40 minutes or until a toothpick inserted into the center of the cake comes out clean. Remove the cake from the oven and place it on a cooling rack.
While the cake is still hot, prepare the glaze by whisking together the powdered sugar, milk, and vanilla extract in a medium bowl. Pour the glaze over the top of the hot cake, using a spatula to spread it evenly over the entire surface. Allow the cake to cool completely before serving.