Prepare the Base: Preheat the oven to 325°F (165°C). In a mixing bowl, combine the cold, cubed butter, white sugar, flour, and pumpkin pie spice. Cut the butter into the dry ingredients until the mixture resembles coarse crumbs. Press the mixture evenly into a 9 x 13-inch baking pan to form the base. Bake for 20 minutes or until lightly golden. Allow it to cool slightly.
Make the Filling: In a double boiler over low-medium heat, combine the sweetened condensed milk, corn syrup, brown sugar, butter, and pumpkin puree. Cook, stirring frequently, until the filling thickens, about 10-15 minutes. Pour the caramel filling over the baked base and let it cool completely.
Prepare the Topping: In a clean double boiler, melt the white chocolate until smooth. Pour the melted white chocolate over the cooled filling layer, spreading it evenly with a spatula. Allow it to set at room temperature or refrigerate briefly for quicker setting.
Cut and Serve: Use a sharp knife dipped in hot water and wiped clean after each cut to slice into squares. This helps prevent the chocolate from cracking. Serve and enjoy!