Preheat the oven to 350°F. Lightly grease a 9x13-inch baking pan and set aside.
In a medium bowl, stir together the cake mix, light brown sugar, and pumpkin pie spice until combined.
In a large bowl, whisk together the pumpkin puree, eggs, sour cream, oil, and vanilla until smooth.
Add the dry ingredients to the pumpkin mixture and stir until combined and no dry streaks remain.
Spread the batter evenly in the greased baking pan.
Bake for 40 to 50 minutes, or until the center is set and a toothpick inserted near the middle comes out clean or with a few moist crumbs.
Allow the cake to cool completely.
Use a fork to poke holes evenly over the entire surface of the cake.
In a medium bowl, whisk together the sweetened condensed milk, evaporated milk, half-and-half, and pumpkin pie spice.
Slowly pour the milk mixture evenly over the cake, allowing it to soak into the holes.
Cover and refrigerate for at least 4 hours, preferably overnight.
Spread the thawed whipped topping evenly over the chilled cake. Sprinkle with pumpkin pie spice, if desired, before serving.